LIBRARY OF CONGRESS. 

(Hjajr.^ ©opjriglji fu .7 

Sheif^..SlX 



UNITED STATES OF AMERICA. 



FAMILIAR TALKS 



ON 



ASTRONOMY. 



FAMILIAR TALKS 



ON 



ASTRONOMY 



WITH CHAPTERS ON 



ffieograpfjg antr Nabtgatton 



EY 



WILLIAM HARWAR PARKER 

AUTHOR OF " RECOLLECTIONS OF A NAVAL OFFICER," ETC. 



#P 




CHICAGO 
A. C. McCLURG AND COMPANY 

i88g 



Copyright 
By A. C. McClurg and Co. 
a.d. i88q 



PREFACE. 



'"THIS little book I have called " Familiar 
Talks ; " it assumes to be nothing more. 
It embodies the gist of the lectures I have been 
in the habit of delivering in the class-room, and 
is written mostly from memory. It is the result 
of thirty years' study, observation, and medi- 
tation. 

I do not pretend to introduce anything new; 
but simply to put some matters in a different 
and, perhaps, more attractive form. I have con- 
tented myself with presenting general facts, and 
have purposely avoided entering into minutice. 
I have, for instance, spoken of the exact dimen- 
sions of the earth, though astronomers say we 
do not know the " exact" dimensions. I have 
spoken of the earth's rotation as being uniform, 
when astronomers say it is " suspected " it may 
not be, etc. 

All such questions, as whether we really know 
the exact dimensions of the earth ; whether its 



vi Preface. 

diurnal motion is absolutely uniform; the con- 
stancy in position of the earth's axis ; the physi- 
cal problems presented by the sun and moon; 
the determination of the parallax of the stars, 
and many similar ones, should be left to the 
specialists who are spending their lives in the 
attempt to elucidate them. This book is not 
written for scientists — who are reckoned by the 
hundred — but rather for the school-boy and 
general reader, who are reckoned by the 
million. 

I have used few diagrams, because I believe 
the student had better think out many matters 
for himself. I have repeated myself frequently 
and intentionally when I particularly wished to 
impress a certain point upon the reader, and 
the quotations are introduced for the same 
purpose. 

The definitions are put in the appendix for 
the student to refer to, though many are em- 
bodied in the text. I can see no more reason 
for putting a collection of definitions in the first 
chapter of an astronomy, than for making a boy 
commit to memory all the words of a Latin 
dictionary before he commences to translate 
Historia Sacra. 

In the last chapter will be found some gen- 
eral remarks on Navigation. The theory by 



Preface. vii 

which a ship's position at sea is found is so 
simple as to be readily comprehended by the 
general reader, and should unquestionably be 
taught to the school-boy. 

It is usual for writers on astronomy to give a 
list of the books consulted by them. While 
writing these talks I have had lying upon my 
desk Lockyer's Elementary Astronomy, and 
Professor White's Elements of Theoretical and 
Descriptive Astronomy. But I have read in 
the last thirty years a great many books on this 
subject. I cannot remember the names of all 
of them. It is not necessary; for, as I have 
said, I do not pretend to give the reader any 
new facts. Indeed, I confess — to use the words 
of Sir Henry Wotton — " I am but a gatherer 
and disposer of other men's stuff." 

I desire to express my thanks to Rear Ad- 
miral S. R. Franklin, Superintendent of the 
Naval Observatory, and to Professor A. Hall, of 
the Observatory, for their kindness in reading 
my manuscript; also, to Professor Keeler, of 
the Lick Observatory. To the last two I am 
indebted for valuable hints. 

Fredericksburg, Va., 
March, 1889. 



CONTENTS. 



TALK THE FIRST. 

PAGE 

The necessity of thought and meditation. Astrono- 
my defined. Its language. The Solar system. 
The ancient astronomers, and what they ob- 
served. Time and the Calendar. Progress of 
the science of astronomy. Pythagoras, Aristar- 
chus, Hipparchus, Ptolemy. The Copernican 
Theory. Galileo, Kepler, and Newton. The 
Earth. Its shape. Its motions. Its size, and 
how determined 15 

TALK THE SECOND. 

The Change of Seasons. The Ecliptic. The Ob- 
liquity of the Ecliptic. Declination. Arctic and 
Antarctic Circles. Tropics of Cancer and Cap- 
ricorn. Solstices. Equinoxes. Apparent motion 
of the Sun. Celestial Poles. Celestial Equator. 
Sun's Distance from the Earth variable. Peri- 
helion and Aphelion. Angular, or Apparent 
Diameter. The Obliquity of the Ecliptic wisely 
ordained. Durations of the Different Seasons. 39 

TALK THE THIRD. 

Long Days and Short Nights, and vice versa. 
Solstices. Equinoxes. Twilight. The Midnight 
Sun. Arctic Voyagers. Appearance of the 



x Contents. 

PAGE 

Heavens to an observer at the Poles ; and at 
the Equator. Velocity of the Earth in its orbit, 
and upon its axis 49 

TALK THE FOURTH. 

The Moon. Its shape. Its size. Its Distance from 
the Earth. Its motions. The Moon's Phases. 
Rule for finding the Moon's age. " Earth-shine," 
or Secondary Light. The Moon's side. Real 
and Synodic Periods. Perigee and Apogee. 
Librations 65 

TALK THE FIFTH. 

The Moon's Angular, or Apparent Diameter. Its 
Distance from the Earth variable. Parallax. 
•Horizontal Parallax. How it is found. Method 
of Computing the Moon's Distance from the 
Earth, and its Diameter and Volume. Light 
shed by the Moon. Nodes. Physical Consti- 
tution of the Moon. Lunar Cycle. Influences. 
Tides. Attraction of Gravitation at Surface. . j8 

TALK THE SIXTH. 

The Sun. Its Shape. Size. Motion. Distance. 
Relative Distances of the Planets from the Sun. 
Transits of Venus. Sun's Parallax. How de- 
termined. Method of finding the Sun's Distance, 
Diameter, and Volume. Disk. Photosphere. 
Point at which Sun rises. . . • • 93 

TALK THE SEVENTH. 

Eclipses. Occupations. A Solar Eclipse. Total, 
Annular, and Partial, Eclipses. Digits. Lunar 
Eclipse. Inclination of Moon's Orbit to Plane 



Contents. xi 

PAGE 

of the Ecliptic. Number of Eclipses in a Year. 
Cycle of Eclipses. Sun's Influences. Its Light 
and Heat - . . . . 105 

TALK THE EIGHTH. 

Recapitulation. The Planets. Those known to the 
Ancients. Discovery of Uranus and Neptune. 
Inferior and Superior Planets. Satellites. Dis- 
covery of the Satellites of Jupiter and Mars. 
Speculations of Bishop Wilkins, and others, con- 
cerning the Moon. The Elephant in the Moon. 
Mercury; its Size, Distance from Sun, and 
Motions. Inferior and Superior Conjunctions. 
Quadratures. Phases. Transits. Venus ; its 
size, distance from Sun, and motions. Phases. 
Transits. Mars; its size, distance from Sun, 
and motions. Opposition and Conjunction. Ju- 
piter. Saturn. Uranus. Neptune. Bode's Law. 
The Satellites of Jupiter. . . . .112 

TALK THE NINTH. 

Recapitulation. Discovery of the Velocity of Light. 
The Asteroids. Are the Planets Inhabited? 
Change of Seasons at Jupiter and Mercury. Ab- 
erration of Light. Kepler's Laws. Determi- 
nation of the Density and Mass of the Earth. 
Density of the Planets. The Planets' Motions 
in their Orbits 134 

TALK THE TENTH. 

The Stars, their Number, Magnitude, Parallax, 
Distance. Colored Stars. The Constellations. 
Geography of the Heavens. Use of Globes. 
The Zodiacal Constellations. Classification of 



xii Contents. 

PAGE 

the Stars. The Milky Way. Double Stars. 
Variable Stars. Star-Clusters. Nebulae. The 
Magellanic Clouds. Meteors. Meteorites. Star 
Showers. Comets. Star-Dials. Precession and 
Nutation 149 

TALK THE ELEVENTH. 

Time. Its Measurement. Standard of Time. Ap- 
parent Solar Day. Sidereal Day. Mean Solar 
Day. Equation of Time. Mean Time and Ap- 
parent Time. The Civil Day. The Astronomical 
Day. Lunar Day. Sidereal Time. Clepsydrae. 
Sun-Dials. Clocks and Chronometers. The 
Week. The Month. Lunar Month. Sidereal 
Month. Calendar Month. Tropical Month. 
Anomalistic Month. Nodical Month. The Year. 
Sidereal Year. Tropical Year. Anomalistic Year. 
Absolute and Relative Time. Local Time. 
Standard Time. 168 

TALK THE TWELFTH. 

International Conference, held at Washington, for 
the adoption of a Single Prime Meridian, and a 
Universal Hour, October, 1884. Explanation of 
the method by which Navigators adjust their time 
when circumnavigating the globe. . . . 187 

TALK THE THIRTEENTH. 

Nautical Astronomy. Astronomical Instruments. 
The Transit Instrument. The Meridian Circle. 
The Prime Vertical. The Mural Circle. The 
Equatorial Instrument. The Nautical Almanac. 
The Early Navigators. The Mariner's Compass. 
Voyage of Columbus. The Trade Winds. The 
Sargasso Sea. Variation of the Compass. . .198 



Contents. xiii 

TALK THE FOURTEENTH. 

PAGE 

The Sextant. Index Correction. Semi-Diameter. 
Dip of the Horizon. Refraction. Parallax. De- 
parture. Course and Distance. Log Book. Log 
and Line. Difference of Latitude, and Difference 
of Longitude. Method of finding the Latitude by 
the Sun's meridian altitude. The Chronometer. 
Method of finding the Longitude by Chron- 
ometer. The Lunar Observation. Charts. Azi- 
muth and Amplitude. Calculation of the Time 
of Sunrise and Sunset. The Artificial Horizon. 
Error and Rate of a Chronometer. Distance at 
which an object is visible at sea. High Water. 
The Merchant Marine. . 217 



APPENDIX. 
Definitions 247 

INDEX 259 



FAMILIAR TALKS 



ASTRONOMY, GEOGRAPHY, AND 
NAVIGATION. 



TALK THE FIRST. 

The necessity of thought and meditation. Astronomy 
denned. Its language. The Solar system. The 
ancient astronomers, and what they observed. Time 
and the Calendar. Progress of the Science of As- 
tronomy. Pythagoras, Aristarchus, Hipparchus, 
Ptolemy. The Copernican Theory. Galileo, Kepler, 
and Newton. The Earth. Its shape. Its motions. 
Its size, and how determined. 

IT is my design to tell you in these talks 
something about the Earth and heavenly 
bodies. I do not propose to write a complete 
treatise on astronomy; but I hope to give you 
an idea, at least, not only of the forms, dimen- 
sions, distances, motions, etc , of the Earth, Sun, 
Moon, planets, and stars, but also of the meth- 
ods by which their orbits and sizes are calculated. 
While I do not expect to tell you anything new 
concerning these bodies, I do intend to try 
to put some subjects before you in a different 



1 6 Familiar Talks on Astronomy ', etc. 

light than that given in our ordinary text-books, 
and I shall endeavor to convey to you as much 
information on this most interesting science as 
will enable you to understand what is usually 
called Descriptive and Practical Astronomy. 
Those desiring to pay especial attention to the 
subject will, of course, proceed to more scien- 
tific works ; and I will be glad to think that this 
little book has led them to give the subject 
more time and attention. 

There is probably no science that requires 
more abstract thought than astronomy, and if 
I succeed in impressing upon you the necessity 
of thinking, I shall not have talked to you in 
vain. 

A recent writer commenting upon the serious 
air of the people generally, — an air of unhappi- 
ness in fact, — says it is occasioned by the too 
constant reading of many books. I am not at 
all sure but that he is right ; perhaps we should 
think more and read less. Carlyle says : — 

" A very small lot of books will serve to nourish a 
man's mind, if he handle them well; and I have 
known innumerable people whose minds had gone 
all to ruin by reading carelessly too many books. . . . 
The wisest men I have known in this world were by 
no means great readers — good readers, I should 
rather say, of a few books that were wise. ... A man 
gathers wisdom only from his own sincere exertions 
and reflections." 



Necessity of Thought. 17 

When we read the lives of Thomas Jefferson, 
James Madison, John Adams, and others of their 
time, we are struck with the great originality 
of thought of these men. They certainly had 
but few books ; but the contents of these books 
they digested well. They spent hours in their 
libraries daily, — not always reading, but think- 
ing. Rousseau says : "Naturally, man thinks but 
little. Thinking is an art which he learns as 
any other, though with more difficulty. I only 
know, in the two sexes, two classes really dis- 
tinct: those who think, and those who do not 
think; and this difference comes almost en- 
tirely from education." Pascal says, "All our 
dignity consists in thought ; " and Gibbon 
says, " The use of our reading is to aid us in 
thinking." 

I will not say that this habit of thinking is 
a lost art ; but I do very much fear that in our 
schools the memory is often cultivated at the 
expense of the understanding, and that the 
scholar is not fully made to comprehend that 
one of the definitions of " study," is meditation. 
The ancient philosophers, of whom our books 
tell us so much, were, after all, I suspect, simply 
" thinking " men. 

The word " astronomy " comes from the Greek, 
and means literally " the law of the stars." We 
define it, however, as " the science which treats 
2 



1 8 Familiar Talks on Astronomy, etc. 

of the heavenly bodies," which you observe 
embraces more ; because all the heavenly bodies 
are not stars, as we shall soon see. 

It is divided into Theoretical, Practical, Nauti- 
cal, and Descriptive Astronomy. Theoretical 
Astronomy explains the rules for calculating the 
masses, motions, and positions of the heavenly 
bodies, and it requires a good mathematician 
to understand and work them. Practical As- 
tronomy applies to the use of instruments. 
Nautical Astronomy is that branch of the sci- 
ence which teaches the navigator to find the 
position of a ship on the ocean. Descriptive 
Astronomy comprehends a general description 
of the heavenly bodies ; of their forms, magni- 
tudes, distances, motions; of their appearance 
and structure; of, in short, everything relating 
to these bodies which comes from observation 
or calculation. 

Our talks will be on Descriptive and Nautical 
Astronomy, with an occasional glance at Theo- 
retical and Practical Astronomy. 

Now I suppose you to be acquainted with the 
terminology, or nomenclature, of this science of 
astronomy. All sciences have a language of 
their own. You know what an algebraic formula 
is. It is a general rule expressed in algebraic 
language ; and when we wish to express it as a 
theorem, we first translate it into ordinary lan- 
guage. For example, in the problem of the 



The Solar System. 19 

couriers, where we desire to know how many 
hours will elapse before the rear courier will 
overtake the one in advance, if we suppose x to 
represent this time, a to represent their distance 
apart, and m and n their respective rates per 
hour, we find — 



which is an algebraic formula, and translated 
means that the time required will be equal to 
the distance of the two couriers apart, divided 
by the difference between their rates of travel. 
And this theorem applies to every possible 
similar problem. 

Well, then, as I say, I suppose you to know 
the language of astronomy, and if you do not 
you must, where I use a word you do not under- 
stand, look it up in the Appendix, precisely as 
you do when you look up the definition of a 
word in your Latin or French dictionaries. 

I suppose, too, that you are all tolerably 
familiar with what is called the Solar System, — 
that is, our System. The Sun being supposed to 
be the centre, all the planets — Mercury, Venus, 
the Earth, Mars, the asteroids, Jupiter, Saturn, 
Uranus, and Neptune — in succession, revolve 
about it in a direction from west to east. They 
all rotate upon their axes in the same direction, 
and those of them that have satellites carry 



20 Familiar Talks on Astronomy, etc. 

them with them in their revolutions about the 
sun. 

This is called the Copernican Theory, and is 
the one universally recognized as the correct 
one. 

You must bear in mind that the stars are 
suns ; they shine by their own light, and prob- 
ably each one is surrounded by planets, and is 
the centre of a system, just as our sun is. But 
this we need not dwell upon here. 

Let us see how this science of astronomy 
began. Who were the first observers of the 
heavens? Shepherds and sailors, of course. 
Their occupations kept them up at night, and 
they naturally observed the heavenly bodies. 
What do any of us in the towns and cities see 
of the heavens, unless we go on the tops of 
our houses, which I am sure we none of us do. 
How different the case with the shepherds on 
the great Eastern plains, or sailors on the broad 
ocean ! They are not only up much at night, 
but they have a clear view of the heavens. 
Moreover, in early times they judged of the 
hour by the positions of the stars and directed 
the course of their ship at night by them. It 
may be that the reason why the Arabians and 
other Eastern nations knew so much about the 
stars was owing to their custom of sitting on 
the tops of their houses at night. Having an 
unobstructed view of the sky they were per- 



Early Observers. 21 

haps led to examine into the motions of the 
heavenly bodies. 

The shepherds, then, were the first astrono- 
mers, or perhaps I had better say, the first 
observers of the heavenly bodies. 

What did they first notice? Naturally, the 
sun. They saw that it was a round, luminous 
body; and that it rose in the east and set in 
the west. 

Next they observed the moon. But here was 
a change. While the sun always presented 
the same appearance, the moon changed from 
a crescent to a circle, and about every thirty 
days it disappeared altogether for a day or two. 
Moreover, its time of rising changed from night 
to night. 

Here was food for thought. It was certainly 
not a self-luminous body, otherwise it would 
not change its apparent shape ; and the change 
in the hour of rising indicated a different mo- 
tion from that of the sun. 

Next our early astronomers turned their at- 
tention to the stars. Here they saw innumer- 
able luminous heavenly bodies rising at all 
points of the compass in the east, between 
north and south, and setting in the west at all 
points between north and south. Some of these 
stars were always visible at night and evidently 
did not set at all. These stars are now called 



22 Familiar Talks on Astronomy, etc, 

circumpolar stars. The farther north or south 
the observer, the more stars there are that do 
not rise or set. We will speak more particularly 
of them farther on. 

They noticed also that the stars preserved 
their relative positions towards each other; 
and that they rose at about the same hour 
every night. A closer and longer observation, 
however, showed them that they really rose 
a little earlier every night, and that, as a con- 
sequence, the aspect of the heavens in the 
course of a year was changed. At any hour, 
say midnight, after an interval of six months, 
an entirely different set of stars was above the 
horizon, — save only the circumpolar stars which 
were always above the horizon. 

But what must have excited the wonder of 
these observers was the fact that although most 
of the stars preserved their relative positions, as 
I have said, there were some, and very bright 
ones too, which wandered among the others. 
They sometimes appeared in one constellation 
and sometimes in another. They may have 
noticed, too, that these bodies did not " twinkle." 
They called them planets, from the Greek word 
signifying to wander. 

Let us now look back and see what our shep- 
herds have noticed : first, the sun ; secondly, 
the moon and its phases ; thirdly, the stars and 
constellations (which are merely groups of 



Natural Standard of Time. 23 

stars); and fourthly, the planets, — all with the 
naked eye. 

Comets, too, they must have occasionally seen, 
moving with great velocity among the stars and 
with long streamers of light behind them ; also 
meteors, those bodies we call " shooting stars." 

They must have observed, also, that the sun 
never rose at exactly the same point in the east ; 
and I may perhaps astonish you when I tell you 
that the sun never does rise due east, and set 
due west, but twice in the year, — i. e. at the 
two equinoxes. This I will explain when I 
come to talk about that luminary. 

The natural standard of time is one revolu- 
tion of the earth upon its axis. This the early 
nations called day and night. The next step 
in their reckoning of time was by the moon. 
You see how naturally this came about. They 
reckoned from one new moon to the next. This 
is what we call a lunar month. You know that 
the American Indians express an interval of 
time as so many " moons," they say, such an 
event occurred a certain number of " moons " 
ago. 

The next step was to find the length of the 
year. This the ancients soon discovered. It 
is said that Thales, one of the seven wise men 
of Greece, first recommended the division of 
the year into three hundred and sixty-five days. 
This was about six hundred years before Christ 



24 Familiar Talks on Astronomy, etc. 

was born. It was not so difficult to discover 
the length of a year (or the time it takes the 
earth to make one revolution about the sun) 
as you may imagine it to be. 

You know the length of the shadow of an 
object, cast by the sun at mid-day is constantly 
changing. The shadow (in the northern hemis- 
phere) cast by any steeple, at noon, is shortest 
on the 2 ist of June (the summer solstice), and 
longest on the 21st of December (the winter 
solstice). You have only to measure these 
shadows, daily, and from the greatest to the 
greatest again, or from the least to the least 
again, is about three hundred and sixty-five 
days. This was the way Thales discovered the 
length of a year, and it is a close approxima- 
tion. By observing the intermediate shadows 
he determined the equinoxes. 

Some time before Caesar it was found that 
the length of the year was not exactly three 
hundred and sixty-five days, but was about 
365 y^ days. You readily see that if we reckon 
the length of the year other than it really is, the 
Calendar, as it is called, must get into a state 
of confusion ; our January might eventually 
come into the middle of summer, and our June 
into the middle of winter. 

Well, in the time of Julius Caesar, about fifty 
years before Christ, the calendar had fallen into 
such confusion that he called in the aid of the 



The Calendar. 25 

Egyptian astronomer Sosigenes, to reform it. 
He assumed the length of the year to be just 
365^ days, and by making every fourth year to 
consist of three hundred and sixty-six days, 
that is, by the introduction of the leap-year, 
it seemed as though the difficulty was solved. 
It would have been if the length of the year 
was exactly 365*^ days; the addition of one 
day every four years (and you know it had to 
be changed a day or twenty-four hours at a time) 
would have kept the calendar perfecty correct. 

The Arabians made great progress in mathe- 
matics and astronomy, and in A. D. 879 Albate- 
gnuis calculated the length of the year to be 
three hundred and sixty-five days, five hours, 
forty-six minutes, twenty-four seconds; which 
is very nearly correct. The exact length is 
three hundred and sixty-five days, five hours 
forty-eight minutes, forty-six seconds; so you 
see that the Julian calendar was itself getting 
into confusion, — very slowly it is true ; but in 
1582 it was found to be in error about eleven 
days. 1 Pope Gregory XIII. had it corrected 

1 By the Gregorian rule every year exactly divisible by 4 is 
a leap-year, excepting the closing years of the centuries, which 
must be divisible by 400 to be taken as leap-years, — thus 1900 
is not a leap-year, 2000 is a leap-year, 2100 is not and so on. 
The year 1900 is the last year of the nineteenth century ; 2000 
the last year of the twentieth century and so on. 

The first day of January, 1901, begins the twentieth century. 
The " London Standard " gives the following explanation why 



26 Familiar Talks on Astronomy \ etc. 

so carefully that it will not be one day in error 
in nearly four thousand years. The Gregorian 
calendar was adopted in England in 1752; and 
this will explain to you why in some old books 
you find two dates given, — Old Style and New 
Style. Russia has not yet adapted the Gre- 
gorian calendar, and the Russian reckoning is 
now twelve days behind ours, — but all the 
other European nations use it, as do all the 
American nations. 

The Chaldeans, Egyptians, and probably, the 
Chinese were the first to make any material 

the year 1900 will not be counted among leap-years. " The 
year is three hundred and sixty-five days, five hours, and forty- 
nine minutes long ; eleven minutes are taken every year to 
make the year 365J days long, and every fourth year we have 
an extra day. This was Julius Caesar's arrangement. Where 
do these eleven minutes come from ? They come from the 
future, and are paid by omitting leap-year every hundred years. 
But if leap-year is omitted regularly every hundredth year in 
the course of four hundred years it is found that the eleven 
minutes taken each year will not only have been paid back, but 
that a whole day will have been given up. So Pope Gregory 
XIII. who improved on Caesar's calendar in 1582, decreed that 
every centurial year divisible by four should be a leap-year 
after all. So we borrow eleven minutes each year, more than 
paying our borrowings back by omitting three leap-years in 
three centurial years, and square matters by having a leap-year 
in the fourth centurial year. Pope Gregory's arrangement is 
so exact, and the borrowing and paying back balance so closely* 
that we borrow more than we pay back to the extent of only one 
day in three thousand eight hundred and sixty-six years." 

The Christian era is said to have been first proposed in the 
year 527 a. d. (Chambers's Enc.) 



AristarckuSy Hipparckus, Ptolemy. 27 

progress in astronomy. Then came the Greeks 
and Arabians. 

Pythagoras, a Greek philosopher, who lived 
about five hundred years before Christ, asserted 
that the earth was not fixed ; but he did not 
know that it revolved about the sun. It was 
Aristarchus, another Greek, who flourished 
about the middle of the third century before 
Christ, who discovered that the earth revolved 
about the sun. It was known as the Pythag- 
orean system, but was not generally accepted 
as true. 

The most famous astronomer before the 
Christian era was Hipparchus, who lived about 
160 B.C. He observed the " precession of the 
equinoxes," catalogued one thousand and eighty 
stars, and calculated eclipses. He determined 
the periods of the planets with a good deal of 
accuracy. His periods of Mercury, Venus, and 
Mars are in error only a few minutes. 

About the year 70, or some say 140, after 
Christ, Ptolemy, a native of Egypt, an astrono- 
mer and geographer of Alexandria, published 
his work, — called by the Arabs the " Almagest." 
He taught that the earth was the centre of our 
system and that the sun, moon, planets, and 
stars revolved about it. This was known as the 
Ptolemaic system and was accepted as the correct 
one. It was in use about fourteen hundred 
years. 



28 Familiar Talks on Astronomy, etc. 

It was, however, reserved for Copernicus, a 
Pole by birth and a priest by profession, to 
establish the system now accepted as the true 
one. Copernicus was at one time a professor 
of mathematics at Rome, and afterwards a 
canon of Frauenberg in Prussia. He conceived 
the theory of the earth's motion about the sun, 
A. D. 1520, but did not dare to publish it until 
the year 1543. This is known as the Copernican 
Theory. Its three fundamental points are: (1) 
that the earth is round; (2) that it turns upon 
its axis from west to east; (3) that the earth 
and other planets revolve about the sun. 

After Copernicus came Galileo, 1 who first used 
the telescope, in 1610; Kepler, who at the same 
time worked out his three grand laws about the 
movements of the planets ; and Newton, who in 
1687 published his great work on Universal 
Gravitation. From this time the science of 
astronomy has made wonderful progress; and, 
what with the improvements of telescopes and 
other astronomical instruments, and the great 
interest exhibited by savans in everything re- 
lating to it, the student finds it difficult to keep 

1 The practical discovery was about 1608. (Enc. Brit.) 
And yet Rogers, in his " Voyage of Columbus," (1492) says ; 

" What long-drawn tube transports the gazer home, 
Kindling with stars at noon the ethereal dome ? " 

And again — 

" But soon the telescope attracts her view." 



The Earth. 29 

up with the discoveries and various theories 
advanced. 

Since it was only in 1543 that Copernicus 
promulgated his system, I call your attention to 
the fact that Columbus (who in 1492 discovered 
America) knew nothing about it, of course. He 
probably believed in the Ptolemean Theory. 
He believed the earth to be round; otherwise 
he would not have expected to reach China and 
Japan by sailing west. He greatly under-esti- 
mated the dimensions of the earth ; and we 
shall see farther on that Sir Isaac Newton, in 
1666, had to suspend his calculations for some 
sixteen years, to wait for a more accurate 
measurement of it. 

THE EARTH. 

The Earth being the planet on which we live, 
is, of course, the one we are most interested in. 
Let us see what we know about it. 

It is round. It is not a perfect sphere; but 
its exact shape is what mathematicians call an 
oblate spheroid, — that is, its polar diameter is 
less than the equatorial diameter. We readily 
see how it assumed this shape. As in the be- 
ginning it was a molten, yielding mass, when it 
was set in motion on its axis it bulged at the 
equator ; precisely as a ball of soft putty would 
do if it should be spun rapidly round its axis. 



30 Familiar Talks on Astronomy, etc. 

How did the ancients know that the earth is 
round? I can give you three reasons : (i) The 
horizon is always a circle ; (2) The shadow of 
the earth thrown on the moon in a lunar eclipse 
is circular; (3) When vessels are observed 
coming in from sea their upper sails are first 
seen, and their hulls last. 

We know a better reason than any of these : 
ships sail around it. Who first sailed around 
the world? Magellan, a Portuguese in the 
service of Spain, in 15 19. He was killed at the 
Philippine Islands; but his ship, under Sebas- 
tian del Cano, completed the voyage. So you 
see that Columbus, although he believed the 
earth to be round, did not know it as we do, 
for up to his time it had not been circum- 
navigated. 

The earth turns upon its axis, from west to 
east, once in 23 hrs. 56 min. 4 seconds. We 
see this by the stars, as we cannot suppose them 
to be revolving about the earth. Moreover, this 
has been graphically illustrated by the French 
philosopher, Foucault, in two ways, — by means 
of a pendulum, and by means of an instrument 
called the gyroscope. 

The pendulum experiment is based upon the 
fact that if a heavy weight is suspended by a 
fine cord, and then swung, it will continue to 
swing in the same plane or same direction, even 



Foucaidfs Experiment. 31 

though the point of suspension be moved. 
Could this experiment be made at the north 
pole, the earth would revolve under the pen- 
dulum once in 23 hrs. 56 min. 4 seconds. 

Foucault's pendulum was suspended from the 
dome of the Pantheon, in Paris, and a fine point 
at the bottom of the weight was made to leave a 
mark in sand at each swing. The experiment 
was also made at Bunker Hill monument some 
thiity-five years ago, if my memory is not at fault. 
You observe that the farther north it is tried 
the more satisfactory the result. At the poles 
the sandy dial would be carried round, under the 
point of the pendulum, once in about 24 hours. 
At the equator there would be no result. 

The experiment with the gyroscope is rather 
difficult to explain, but the result is the same ; 
the earth is shown to turn upon its axis from 
west to east. 

The earth is a non-luminous body. This 
needs no proof. To " the man in the moon " 
the earth presents the same appearance that the 
moon does to us. It shines by the reflected 
light of the sun, and exhibits phases; that is, 
it appears crescent-shaped, gibbous, and full. 
But it never sets, l and appears four times as 

1 It never sets because the moon always presents the same 
side to us, as we shall see farther on. To an inhabitant of this 
side of the moon, the earth, of course, would be always visible. 



32 Familiar Talks on Astronomy, etc. 

large as the moon does to us. What a mag- 
nificent spectacle ! 

The polar diameter of the earth is about 7900 
miles, and the equatorial diameter 7926 miles. 
How did astronomers measure these diameters? 
They cannot be measured directly, as you know, 
but if we can discover the circumference of a 
circle we can calculate the diameter. How did 
astronomers measure the circumference of the 
earth, when no traveller has been within 400 
miles of the north pole, and not nearly so close 
to the south pole? We are told that Eratos- 
thenes, B. c. 276, was the first to attempt to 
measure the size of the earth. 1 He was not so 
much an astronomer as a geographer. 

Eratosthenes calculated that the distance be- 
tween Syene and Alexandria (Egypt) was one- 
fiftieth of the whole circumference of the earth. 
He found this out by an attempt to discover the 
the angular difference of latitude between the 
two places. He then measured the distance 

1 The Encyclopaedia Britannica says on this point : " It 
had been ascertained by the surveyors of Alexander and the 
Ptolemies that the itinerary distance between Syene and Alex- 
andria was 5000 stadia. Hence, 5000 X 50 = 250,000 = cir- 
cumference of the earth. Unfortunately, on account of the 
uncertainty respecting the length of the stadium here employed, 
we possess no means of estimating the degree of approxima- 
tion afforded by this rude though ingenious attempt." 

Webster says the stadium = 606 ft. 9 in. Assuming this to 
be correct, and taking the geographical mile to be 6016 feet, 
we find the circumference to be 24,924 miles. 



Earttis Measurement. 33 

between them, and found it to be 625 miles. 
625 multiplied by 50 gives 31,250 miles for the 
circumference of the earth, which is as nearly- 
correct as could be expected with the means at 
his command. He measured the difference of 
latitude by means of what the Greeks called a 
gnomon, an upright pillar which was used by 
them to measure the sun's altitude by means of 
its shadow. He made many errors in his ob- 
servations. He took Syene, or Assouan, as it is 
now called, to be in lat. 23 30' N., because he 
observed that the gnomon cast no shadow there 
at the time of the summer solstice, when it is 
directly overhead to persons in that latitude. 
His observation was erroneous, for Assouan is 
in latitude about 24° north. Moreover, he sup- 
posed Assouan and Alexandria to be on the 
same meridian, which is far from being the 
case; and lastly, he largely over-estimated 
the distance between them. 

It is on the same principle that astronomers 
have since arrived at the exact dimensions of 
the earth. They have found the length of one 
degree of latitude to be sixty geographical 
miles; 60 multiplied by 360 equals 21,600 
miles, which is about equal to 25,000 statute 
miles; and this in round numbers is the dis- 
tance around the earth at the equator. Of 
course it is less, in an east and west direction, 
as we approach the poles. Knowing the cir- 
3 



34 Familiar Talks on Astronomy, etc. 

cumference of a circle we have only to divide 
it by 3.1416 to find its diameter. 

Now you are not to suppose that it was so 
easy to arrive at the length of one degree of 
latitude. The greatest mathematicians of the 
world have been employed in this work, — and 
yon will recognize the importance of finding the 
dimensions of the earth in the most exact manner 
when I tell you that the distances and magnitudes 
of all the other heavenly bodies depend upo7i it. 
Nor must you imagine that a distance of sixty 
miles is actually measured on the surface of the 
earth with a line or measuring-rod. A base- 
line of, say, ten miles is measured, and then by 
a system of triangulation the distance between 
the extreme points is calculated. 

The measurement of the base-line alone is 
the labor of months. The ground has to be 
selected, and instruments have been invented 
to measure it with the utmost nicety. The 
Reports of the United States Coast Survey 
contain interesting information on this point. 

In the diagram (Fig. 1), suppose we wish to find 
the distance between the points A and B. We 
measure the distance B N ; this is our base-line. 
We then place theodolites at B and N, select 
some point as M, and measure the angles M B 
N, and B N M. Then in the triangle B M N, 
knowing a side and the angles, we calculate the 
length of the side B M. We now remove the 



Method of Triangulation. 



35 



theodolite from N to M, select some point, as 
L, and measure the angles L B M and B M L 
and calculate the sides L B 
and L M. Remove the the- 
odolite from B to L, select 
some point, as K, and measure 
the angles KLM and L M 
K, and calculate the side K L. 
Remove the theodolite from 
M to K, select some point, H, 
measure the angles H L K 
and H K L, and calculate the 
sides H L and H K. Proceed 
in this manner until A is 
reached, and the sum of the 
sides B L, L H, H F, F D, 
and D A, will be the distance 
between the points A and B 
required. 

The points L, H, F, D, need 
not necessarily be on the me- 
ridian line A B ; the diagram 
is drawn simply to illustrate 
the method. I cannot enter 
into the minutice of the work, 
as it would require a small 
volume in itself. 

One thing you see ; and that is, if we actually 
measure the last distance A D, and compare it 
with the calculated distance, it is a test of the 




Fig. i. 



36 Familiar Talks on Astronomy, etc. 

correctness of the triangulation. This is called 
a verification base. 

When Newton first attempted to work out 
the Law of Universal Gravitation he found his 
calculations came out wrong. This was in con- 
sequence of an error in determining the size of 
the earth. Not that the error had been made 
by Newton himself, — he never attempted to 
measure it, — but he took the figures which 
were accepted as true at the time. Sixteen 
years after (in 1682), a French astronomer 
named Picart measured an arc of the meridian, 
and Newton adopting his figures discovered the 
law. This patience on the part of Sir Isaac 
in laying aside his computations for so many 
years, and waiting for further information, is 
even greater than that he exhibited when his dog 
Diamond destroyed his notes on Chemistry. 

Some time after this, Cassini asserted that the 
degrees of longitude varied in length 1 and that 
the earth was a prolate, and not an oblate 
spheroid ; that is, that its polar diameter was 
greater than its equatorial diameter. To settle 
the controversy, France and Spain, in 1735, 
sent a commission to Peru to make a new 
measurement; and a party was sent to Lap- 
land at the same time to measure an arc in 
that latitude. The principal French and Span- 
ish mathematicians were La Condamine and 

1 Meaning, of course, on the same parallel of latitude. 



An Arc of the Meridian. 37 

d'Ulloa. Maupertius and Celsius were of the 
northern party. The arc measured in Peru was 
in mean latitude i° 31' S. ; and the one in 
Lapland in about 66° N. The length of the 
degree in Peru was found to be 362,790 feet; 
while the length of the degree in Lapland was 
365,744 feet. 

Since that time measurements of an arc of 
the meridian have been made in Sweden, Russia, 
Prussia, Hanover, Denmark, England, France, 
Italy, India, and the United States. The least 
arc measured was 57', and the greatest 15 57'. 
All done by triangulation, as I have said. From 
these measurements the length of one degree in 
different latitudes has been found. 

The measurement of the arc in the United 
States was done in 1764 by Mason and Dixon, 
the same surveyors who ran the line to determine 
the boundary line between Pennsylvania and 
Maryland. You have all heard of " Mason and 
Dixon's line." 

The length of one degree of latitude in Lap- 
land is 2,954 feet more than the length of one 
degree near the equator, you observe. Why is 
this? If the earth were a perfect sphere, the 
length of one degree would be the same in all 
latitudes ; and the very fact that the degrees are 
longer as we approach the poles proves that the 
earth is flattened at the poles, and hence is an 
oblate spheroid. Sir Isaac Newton deduced this 



38 Familiar Talks on Astronomy, etc. 

from his law of gravitation before any measure- 
ments had been made to investigate it. 

Let us now look back and see what we have 
discussed in this talk. 

1. The necessity of thought and meditation. 

2. The definition of astronomy, and its 
language. 

3. What the earliest astronomers must have 
first observed. 

4. Time, and the Calendar. 

5. Progress of the Science of Astronomy. 

6. The Earth, — its motions, its shape and 
size, and how determined. 

I hope that I have not made this talk so long 
as to tire you ; but I hope still more that I have 
made plain what I have attempted to explain, 
and that I have conveyed no false ideas ; for, as 
Pope says, — 

" Of the two, less dangerous is the offence, 
To tire our patience, than mislead our sense." 



TALK THE SECOND. 

The Change of Seasons. The Ecliptic. The Obliquity 
of the Ecliptic. Declination. Arctic and Antarctic 
Circles. Tropics of Cancer and Capricorn. Solstices. 
Equinoxes. Apparent Motion of the Sun. Celestial 
Poles. Celestial Equator. Sun's Distance from the 
Earth variable. Perihelion and Aphelion. Angular, 
or Apparent Diameter. The Obliquity of the Ecliptic 
wisely ordained. Durations of the different seasons. 

FHE earth not only rotates about its axis, 
but it also revolves about the sun, in an 
elliptical orbit, once in 365 days, 5 hrs., 48 min., 
46 seconds. This we call a year. The change 
in the length of our days, and the change of our 
seasons, are a consequence of the earth's motion 
around the sun. 

Aristarchus, 1 B. C. 270, discovered that the 
axis of the earth was not perpendicular to the 
plane of the ecliptic ; and that this obliquity of 
the ecliptic, as it is called, was the cause of the 
change of seasons as the earth pursued its path 
about the sun. Let us inquire into this change 
of seasons, and see how it is caused. 

1 Aristarchus was the first to endeavor to find the sun's 
distance from the earth. 



40 Familiar Talks on Astronomy, etc. 

The path of the earth around the sun is 
called the ecliptic. It came to be named the 
ecliptic, because when the sun or moon is 
eclipsed, it is in this circle. This we shall see 
when we come to talk about eclipses. 

Now, the earth's axis is not set perpendicular 
to the plane of the ecliptic. If it were, the 
equator and ecliptic would lie in the same 
plane. The axis is inclined so as to make the 
angle between the equator and ecliptic about 
2^y 2 degrees. This limits the sun's declina- 
tion to 23^ degrees; and it is this obliquity 
of the ecliptic, too, that places the Arctic 
and Antarctic circles 23^ degrees from the 
poles, and the tropics of Cancer and Capri- 
corn 23^ degrees from the equator. When 
I was a boy I used to wonder why geogra- 
phers did not place these imaginary circles at 
23 or 24 degrees, and not bother us with the 
fraction. 

The axis of the earth points always in the 
same direction. Hence, at our summer solstice, 
June 21, it is inclined toward the sun to its 
greatest possible extent ; and at our winter 
solstice, December 21, it is inclined from the 
sun to its greatest possible extent. On the 2 1st 
of June, then, the North Frigid zone is entirely 
illuminated, and it is constant day; the South 
Frigid zone receives no light from the sun, and 
it is constant night. 



The Seasons. 



4i 



On the 2 1 st of December the North Frigid 
zone receives no light, and it is constant night ; 
while the South Frigid zone is entirely illumin- 
ated, and it has continual day. 

At the equinoxes, March 21 and September 
21 (that is, when the sun crosses the equator), 
one half of the earth is illuminated from pole 
to pole. 




Fig. 2. 



Note. It is to be noted that this figure, like all others in 
the book, is out of scale, and very much exaggerated. The 
earth's orbit, for example, is represented as a circle, though we 
know it to be an ellipse. 



42 Familiar Talks on Astronomy \ etc. 

In the diagram (Fig. 2), let S be the sun, and 
A, B, C, D, the earth in four positions in its 
orbit ; P P' the axis of the earth, and E Q the 
equator. A represents it on the 21st of June, 
C on the 21st of December, B on the 21st of 
September, and D on the 21st of March. Let, 
also, a b and a' b' be the Arctic and Antarctic 
circles. At A, the summer solstice, the North 
Frigid zone is entirely illuminated, and the days 
are evidently longer than the nights everywhere 
in the northern hemisphere. At C, the winter 
solstice, the North Frigid zone will receive no 
light from the sun, and the days in the northern 
hemisphere are shorter than the nights. At B, 
the autumnal equinox, and at D, the vernal 
equinox, the earth is illuminated from pole to 
pole, and the days and nights are equal all 
over the world, — which, indeed, is the reason 
why these points are called the equinoxes. At 
the equator the days and nights are always 
equal. 

If you will attentively study the diagram, you 
will see all this very clearly; and you will see 
also that the seasons in the southern hemi- 
spheres are just the reverse of ours. When I 
said the sun " crosses the equator," I referred to 
the apparent motion of the sun. It is the earth 
that moves. We very frequently speak of the 
sun moving, meaning its apparent motion. Thus 
we say the sun rises and sets ; but we know that 



Change of Seasons. 43 

it is the motion of the earth upon its axis that 
causes it to rise and set. And I will take occa- 
sion here to tell you that the prolongation of 
the earth's axis to the sphere of the heavens 
marks what we call the celestial poles, and the 
extension of the plane of the equator is the 
celestial equator, or the equinoctial. 

But what causes the change of seasons? Is 
it because we are nearer the sun at some times 
than at others, the orbit of the earth being an 
ellipse with the sun in one of the foci? No, 
strange to say, that has nothing to do with it. 
We are, in point of fact, nearer the sun in Jan- 
uary than in July. 

The change of seasons is caused by the differ- 
ent angle at which we receive the sun's rays. 
In summer the sun attains its greatest altitude, 
we receive the rays more perpendicularly, and 
it is warm. In winter the sun is at its least 
altitude, we receive the rays more obliquely, 
and it is cold. At the equator the sun is never 
very far from the zenith, there is very little 
change in the seasons, and it is always warm. 
At the poles the sun never attains a greater 
altitude than 23^°, the rays are oblique, and 
it is generally cold. Moreover, in our summer 
the days are longer than the nights, and we 
have more of the sun's heat. In fact, from the 
time the sun crosses the equator on March 21, 
the days in the northern hemisphere are longer 



44 Familiar Talks on Astronomy, etc. 

than the nights, until it crosses it again on the 
2 ist of September. 

So we see the change of seasons is caused by 
the revolution of the earth about the sun, and 
the obliquity of the ecliptic. 

I said that we are nearer the sun in January 
than in July. How do we ascertain this fact? 
The proof is very simple. You will see it in 
a minute. You know that if you hold an 
orange or anything else in your hand it ap- 
pears larger when brought close up to the eye 
than when at a distance. The farther off it is 
held, the smaller it appears. That is, its angu- 
lar diameter is less. By angular diameter we 
mean the angle it subtends at the eye. 

Now when we measure the sun's angular 
diameter with a sextant, or other astronomical 
instrument, we find it to be greatest in January, 
and least in July ; ergo the sun is nearest us in 
January, and farthest in July. When nearest 
the earth it is said to be in perihelion, and when 
farthest in aphelion. 

You must not confound the angular diameter 
of a body with its real diameter. The former 
depends upon its distance and is measured in 
degrees, minutes, and seconds of arc; and, in 
the case of the sun, moon, and planets, is con- 
stantly changing; the latter is in miles and is 
of course always the same. 

I have said that in the southern hemisphere the 



The Earth's Axis. 45 

seasons are the reverse of ours, — their winter 
is our summer, their spring our autumn; but 
I will call your attention to the fact that the 
inhabitants of that hemisphere are nearest the 
sun in their summer, and farthest off in their 
winter. This should make, in corresponding 
latitudes, their winters colder than ours and their 
summers warmer; and, indeed, Captain Sturt, 
who explored Australia, describes the heat in 
the interior of that vast island as beyond any- 
thing we have any conception of in our temper- 
ate zone. 

Having explained to you the cause of the 
change of our seasons, I wish now to show you 
that this inclination of the earth's axis to the 
plane of the ecliptic has been ordained by a 
wise Providence. To illustrate this, I will make 
two suppositions : first, let us suppose that the 
axis of the earth lay in the plane of the ecliptic. 
The equator would then be at right angles to it. 
What would be the change in the seasons? 

When the earth was in that part of its orbit 
directly east of the sun it would be illuminated 
from pole to pole, and the days and nights 
would be equal all over the world. As the 
earth moved northward, the southern hemi-. 
sphere would receive more and more of the 
light of the sun, and the northern hemisphere 
would lose it, commencing at the pole. The 



46 Familiar Talks on Astronomy, etc. 

days would be growing longer in the southern 
hemisphere, and shorter in the northern one. 
When the earth was due north of the sun, the 
southern hemisphere would have a vertical sun, 
and constant day; and it would be intensely 
warm. The northern hemisphere would have 
no sun at all ; it would be constant night, and 
intensely cold. As the earth moved on in its 
orbit, the northern hemisphere would receive 
more and more of the sun's rays, commencing 
at the equator, and the southern hemisphere 
would lose them. The days would be growing 
longer in the northern hemisphere and shorter 
in the southern one. When the earth was due 
west of the sun it would be illuminated from 
pole to pole, as in its eastern position, and the 
days and nights would be equal again all over 
the world. As the earth moved on, the south- 
ern hemisphere would lose the sun's light, com- 
mencing at the pole, and the northern one would 
receive more and more of it. The days would 
be growing shorter in the southern hemisphere 
and longer in the northern one. When the earth 
was due south of the sun, the northern hemi- 
sphere would have constant day, and extreme 
heat; and the southern one wpuld have constant 
night, and intense cold. 

It is readily seen that under this supposition 
the change of seasons would be too violent ; and 
neither animal nor vegetable life could subsist. 



Change of Seasons. 47 

Secondly, let us suppose the axis of the earth 
to be perpendicular to the plane of the ecliptic. 
The plane of the equator would then coincide 
with the plane of the ecliptic. Let us see what 
the change in the seasons would be. 

In this case one half of the earth, from pole 
to pole, would be illuminated at all times of the 
year. It would not matter in what part of its 
orbit the earth happened to be. The days and 
night would be equal all over the world, at all 
times of the year. The torrid zone would enjoy 
perpetual summer ; the temperate zones, spring ; 
and the frigid zones, winter. That is, what we 
call these zones. Under the supposition there 
would be no Arctic and Antarctic circles, and 
no tropics of Cancer and Capricorn. There 
would be nothing to indicate these imaginary 
circles in either of my suppositions. The only 
change of seasons in this last case would be 
that owing to the difference in distance of the 
earth from the sun as it went round in its 
elliptical orbit. This would be so slight that 
we may say there would be no change of 
seasons. 

In what we call the torrid zone animal and 
vegetable life could subsist under these circum- 
stances ; but probably not in what we call the 
temperate and frigid zones. 

These two cases may be very easily illustrated 
by taking an apple to represent the earth and 



48 Familiar Talks on Astronomy, etc. 

thrusting a knitting-needle through the core to 
represent its axis. Let a candle be placed at 
the centre of a round table to indicate the sun, 
and the plane of the table will be the plane of 
the ecliptic. First, place the needle horizon- 
tally at the edge of the table, and carry the 
apple around the table, keeping the needle 
pointing always in the same direction, — and 
you will see the change of seasons as described 
under my first supposition. 

Secondly, place the needle perpendicular to 
the table, and move the apple around it, and 
you will see at once that there can be no change 
of seasons, and that the days and nights must 
be equal all over the world at all times, as I 
have said. 

The thoughtful student may inquire why the 
different seasons, — spring, summer, autumn, 
and winter, — are of unequal duration. If the 
earth moved with a uniform motion, in a circu- 
lar orbit, this inequality would not exist. But 
the earth moves in an elliptical orbit, with the 
sun in one of its foci, and with variable veloci- 
ties. In winter the earth has not only a shorter 
arc to pass over, but it is moving with a greater 
velocity than in summer. 

Mons. Guillemin reckons the mean durations 
as follows: spring, 92.9 days; summer, 93.6 
days ; autumn, 89.7 days ; winter, 89 days. 



TALK THE THIRD. 

Long Days and short Nights, and vice versa. Solstices. 
Equinoxes. Twilight. The Midnight Sun. Arctic 
Voyagers. Appearance of the Heavens to an Observer 
at the Poles ; and at the Equator. Velocity of the 
Earth in its Orbit, and upon its Axis. 

LET us now look into this matter of long 
days and short nights, and vice versa. 

You know that our longest day is the 21st 
of June, when the sun is in that sign of the 
zodiac called Cancer, — hence the tropic of 
Cancer. The sun on that day attains its great- 
est distance north of the equator. This distance 
from the equator is called its declination, and 
its greatest possible is 23 J^ degrees; because 
that is the inclination of the equator to the 
ecliptic, as I have already told you. 

Now when the sun is near its greatest declina- 
tion it varies very little in its time of rising, and 
in its meridian altitude, from one day to another. 
For a few days before and after June 21 it rises 
at about the same hour, and attains about the 
same meridian altitude. This is simply owing 
to the fact that it changes its declination very 
4 



50 Familiar Talks on Astronomy ', etc. 

little from day to day. It is said that Thales, 
B. C. 600, observed this. He called it the sol- 
stice, from sol, the sun, and stare, to stand. Thus 
December 21 is our winter solstice and, theo- 
retically, our coldest day; and June 21 our 
summer solstice and, theoretically, our warmest 
day. You remember that Scott says in the 
Lady of the Lake : — 

" And not the summer solstice there 
Tempered the midnight mountain air." 

Let us take a certain day of the year, say the 
2 1st of June, when the sun's declination is 
233^ degrees north, and suppose four observers; 
A, B, C, D, to be at different points on the 
earth's surface. We will suppose A to be at 
the equator ; B to be in latitude 23^° N. ; C 
to be in latitude 6o° N. ; and D to be in lati- 
tude 66yi° N., — that is, on the Arctic circle. 

On the 2 1st of June the days are longer than 
the nights everywhere in the northern hemi- 
sphere, as we have seen. Between the ver- 
nal and autumnal equinoxes the days in the 
northern hemisphere are longer than the 
nights ; and the reverse in the southern hemi- 
sphere. Let us look at our observer A. His 
days and nights are equal. The sun rises at six 
in the morning, and sets at six in the evening. 
It bears at rising east-northeast, and at setting 
west-northwest. 



Long Days and Short Nights. 51 

Now let us look at our observer B. As his 
latitude is the same as the declination of the sun, 
the latter will be, at noon, directly over his head, 
— that is, in his zenith. Here I will call your 
attention to a singular fact: as the observer's 
latitude is the same as the declination of the 
sun, you would naturally expect the sun to rise 
in the east point and set in the west point of 
the compass. But this is not so ; it rises a 
little to the northward of east-northeast and 
sets a little to the northward of west-northwest ; 
and, what is more, it will continue to rise more 
and more to the northward and to set more and 
more to the northward as we proceed north ; 
though it will always be south of us at noon. 
This is owing to the obliquity of the ecliptic, 
which I have said so much about. 

To B the sun will rise at 20 minutes past 5 in 
the morning, and set at 40 minutes past 6 in the 
evening. His days will be 13 hrs. 20 min. long, 
and his nights 10 hrs. 40 min. long. 

Let us now go to our observer, C, in latitude 
6o° N. Here the sun at rising bears north- 
northeast, and at setting, north-northwest. It 
rises at a quarter before 3 in the morning, 
and sets at a quarter past 9 in the evening. 
The day is 18 hrs. 30 min. long, and the night 
but 5 hrs. 30 min. long. But in consequence of 
the "twilight'' our observer would have no 
night at all ; or, I had better say, he would have 



52 Familiar Talks on Astronomy, etc, 

no darkness. He would be able to read a book 
at midnight without the aid of artificial light. 

Let us see what twilight is. It is due to the 
reflective power of the atmosphere. If the at- 
mosphere did not reflect light, we would be in 
darkness whenever we passed out of the direct 
rays of the sun ; and the transition from day to 
night would be instantaneous, and there would 
be no such thing as twilight. 

Now, an observer sees some of the reflected 
rays of the sun until it has reached a circle 1 8 
degrees below the horizon. This circle is called 
the crepusculum. The duration of twilight de- 
pends upon the latitude of the observer and the 
declination of the sun. 1 It is a simple problem 
to work out. We first calculate the time of the 
sun's setting. This we do by solving a right- 
angled spherical triangle, of which we have 
given two sides, viz. : the latitude, and the com- 
plement of the declination of the sun, or the 
polar distance, as it is called. With the two 

1 A writer in the New York "Home Journal," of April io, 
1889, speaking of the Azores, or Western Islands, which are in 
38 north latitude, says : " It was the first day of June when 
we arrived at Fayal. In these southern (sic) latitudes balmy 
summer twilights close in the dark shadows of night almost 
without warning. There is no afterglow ; no tender gloaming, 
no lengthening out of daylight." And again, in a letter of 
May 1, the same writer says of Fayal (latitude 38 north) : 
" The fish caught in these southern (sic) waters exceed in bril- 
liant coloring their comrades of northern climes." And this 
from Boston ! ! 



Twilight. 5 3 

known sides, then, we compute the angle at the 
pole, and this is the sun's hour angle, or the 
local time of sunset 

We then suppose the sun to be 18 degrees 
below the horizon, and again find the sun's hour 
angle. We have in this case to solve an oblique 
spherical triangle, of which we have given 
the three sides, viz. : the complement of the 
latitude, and the sun's polar distance, as before, 
and the sun's altitude, which is minus i8°. The 
hour angle, when found, will be the time of the 
end of twilight; and the difference between this 
time and the time of sunset will be the duration 
of twilight. 

Now to our observer C, in latitude 6o° N., the 
sun will not, after setting, go as far below the 
horizon as 1 8 degrees, and he will have twilight 
all night, as I have said. In the tropics, that is, 
to an observer in the tropics, the sun descends 
nearly at right angles to the horizon, and soon 
reaches the crepusculum ; hence the twilight is 
short. In high latitudes the sun descends 
obliquely, and takes longer to reach the crepus- 
aditm; hence the twilight is long. It is least at 
the equator, and greatest at the poles. 

We will now join our observer D, whom we 
supposed to be in latitude 66 l A° N., or on the 
Arctic circle. His day would be 24 hours long. 
The sun would not set at all. At noon it would 
bear due south, and would be 47 degrees high, 



54 Familiar Talks on Astronomy, etc. 

that is, 47 degrees above the horizon. It would 
then descend, in an oblique direction, towards 
the horizon, and moving to the northward and 
westward, would at midnight just touch the 
horizon, and bear due north. 1 It would then 
commence to rise again and begin another day. 
(I am neglecting the effect of refraction, which 
I will explain farther on.) This is what is 
called the " midnight sun." It is customary 
for the English tourists to go every summer to 
Norway to observe it. Not that this spectacle 
is peculiar to Norway. Do not get that idea 
into your heads. You can see the midnight 

1 And yet this paragraph has been going the round of our 
papers, unquestioned. It is hardly necessary to say that if the 
observer was "looking west," he would not see the sun at all ; 
still less would he see it rise there: — 

"Sunset and Sunrise in Norway. — Imagine yourself in a 
ship at anchor looking west, or straight in front of you. There is a 
broad expanse of sea a little to your right hand, behind you will be the 
rugged coast, and to your left the long, narrow fiord between the islands 
and the main land that the steamer has just traversed. You watch the 
sun as it slowly, slowly sets ; the islands and the coasts look like a dark 
rich purple, and the shadows cast by the ship's masts grow longer and 
longer. After a bit, when the sun has sunk apparently twelve feet from 
the horizon, it stops and seems to remain stationary for about twenty 
minutes ; then the very seagulls hide away, while the air all of a sudden 
strikes chilly. Each one has an awed, expectant feeling. Anon the 
sun rises very slowly once again, and the yellow clouds change with 
his uprising to even greater beauty ; first to the palest primrose and 
then to a bluish pink. The sky, which was just now rose-color, be- 
comes gray, then pale emerald green, and eventually rock after rock 
stands out, caught by the sun's rays, and the reign of day has begun 
once more." — From " A Jubilee Jatint." 



The Midnight Sun. 55 

Sim anywhere on the Arctic circle on the 21st 
of June. Europeans go to Norway to observe 
it, because Norway is accessible. Americans 
might go to Greenland to do so, and I wonder 
our " sight-seers " do not. You have perhaps 
read Du Chaillu's book, entitled, " The Land of 
the Midnight Sun." He applies the name to 
Norway and Lapland ; but, as I have just said, 
these countries are no more entitled to it than 
Greenland, Siberia, or Alaska. 

I read once of an Englishman who journeyed 
to Norway expressly to see the midnight sun. 
He gave his servant orders to call him long 
enough before midnight to give him time to rise 
and dress. Upon being called, he turned over 
in bed and remarked that he really felt too tired 
to rise, " but that he would come back again 
next year ! " If any of you should ever go to, 
say, Discoe, in Greenland, to observe this in- 
teresting spectacle, I hope you will not imitate 
this Englishman's bad example. 

But you must not gather from what I have 
said that the midnight sun is only to be seen on 
the Arctic circle. As soon as the sun has 
crossed the equator, on March 21, the whole 
of the north pole is illuminated, and, as the 
sun's declination increases, so does a corre- 
sponding portion of the earth's surface about 
the pole receive more and more light. For 
example: on May 1 the declination of the sun 



56 Familiar Talks on Astronomy, etc* 

is 1 5 N., and a zone 15 degrees from the north 
pole is constantly illuminated. Within this 
circle it is continual day, and the inhabitants 
have a midnight sun. If a man wished to be on 
the circle where he could just see it, — as in the 
case of our observer on the Arctic circle on 
the 2 1st of June, — he would have to be on the 
1st of May in latitude 75 N. This, to fully 
comprehend, you must think out for yourselves. 
Let us go back again to our observer whom 
we left on the Arctic circle on the 21st of June, 
The sun now begins to move toward the equa- 
tor ; its declination decreases daily ; and if 
our observer should travel north just as many 
degrees or minutes as the declination decreases, 
he would continue to see the sun just grazing 
his northern horizon at midnight. Suppose that 
on the 2 1 st of June he had been in latitude 
75 30' N., instead of in latitude 66° 30' N. The 
sun at noon would have been 38 above the ho- 
rizon, bearing south ; and at midnight it would 
have been 9 above the horizon, bearing north. 

At the poles the days are six months long, 
and the nights the same. At the north pole 
the day begins at the vernal equinox, and 
ends with the autumnal equinox. But twilight 
at the poles lasts one and a half months ; and 
" refraction " also assists to make the days a 
little longer. 



Arctic Voyagers. 57 

You have all read of the Arctic voyagers and 
their long nights. In latitude 78 north the 
night is four months long; that is, the sun is 
that time below the horizon. Fortunately the 
moon, unlike the sun, changes its declination 
very rapidly, so that in the course of a year it 
crosses the equator very often. And whenever 
it is far enough from its extreme southern decli- 
nation, our voyagers will be cheered by its light. 
To an Arctic voyager in latitude jZ° N. the 
moon would be visible as soon as it attained a 
declination of 12 south; and after it attained a 
declination of 12° north it would not set at all. 
There would be a moon bearing south, and a 
moon bearing north, just as we have seen with 
the sun. 

Of course the return of the sun is anxiously 
looked for by these hardy mariners; and about 
the time it may be expected to be seen, all hands 
are on the lookout for it. Some go aloft, so that 
they may be the first to see it. You know as 
well as I do that the higher we ascend the farther 
we can see. This is owing to the fact that the 
earth is a sphere ; and when I come to explain 
to you what we call the " Dip of the Horizon," 
I will tell you how much farther we can see; 
but this by the way. On one of the ships sent 
to look for Sir John Franklin (who, you recol- 
lect, went in 1845 with two ships to search for 
a northwest passage to the Pacific Ocean, and 



58 Familiar Talks on Astronomy, etc. 

who with all of his officers and men perished), 
the officers edited for the amusement of the 
crew a small sheet called the " Illustrated Arctic 
News." One of the pictures represented the 
sun just peeping above the southern horizon. 
In the foreground was a ship frozen up in the 
ice, and near by was a party of sailors gazing 
intently at the sun, throwing their caps in the 
air and dancing for joy. It was called " The 
Prodigal's Return." 

Now if I have made myself plain, and if you 
will draw a few diagrams to assist you, and 
then give this subject some hours' thought, I 
am sure you will fully comprehend this matter 
of the length of the days in different latitudes, 
which, simple as it is, seems not to be generally 
understood. 

After the 2ist of June the days in the north- 
ern hemisphere grow shorter and shorter until 
the autumnal equinox, September 21, when the 
days and nights are equal all over the world. 
From this time until the vernal equinox our 
nights are longer than the days. And in the 
southern hemisphere the seasons are the reverse 
of ours, which I have purposely repeated more 
than once. 

Where would a man go on the earth's surface 
in order to see all the stars in the heavens? To 



An Observer at the Pole. 59 

the equator; for there he would see, in the 
course of six months, all the visible stars from 
the north pole to the south pole. I am suppos- 
ing the observer to view the stars with the naked 
eye, at night only. 

Where would he go to see the least number? 
To the poles ; for at the north pole he would 
see only the stars of the northern hemisphere, 
and at the , south pole those belonging to the 
southern hemisphere. At intermediate points 
he would see more or less, as he approached 
or receded from the equator. 

In latitude 40 north we see all the stars of 
the northern hemisphere, and all those belong 
ing to the southern hemisphere which are not 
nearer the south pole than forty degrees. 

Let us suppose a man to be at the north pole, 
and see what the appearance of the heavens 
would be to him. The north star, Polaris, would 
be nearly in his zenith ; that is, nearly overhead. 
If it were exactly at the pole of the heavens, it 
would be directly in the zenith ; but it is really 
about i° 18' removed from the pole. We will, 
however, neglect this, and consider it to be in 
the zenith of our observer. 

All the other stars in the northern hemisphere 
would be always above his horizon, and his hori- 
zon would be the plane of the equator. The 
stars would not rise or set. but would move 



60 Familiar Talks on Astronomy, etc. 

around our observer in circles parallel to the 
horizon. They would all be circumpolar stars. 
A star of no declination would go around on 
the horizon, and all the others would describe 
circles parallel to it, at altitudes corresponding 
to their declinations. 

If the sun were north of the equator, — that 
is, any time between March 21 and September 
21, — it would be constant day, and the sun it- 
self would go round in a circle parallel to the 
horizon, and at a height above it corresponding 
to its declination. On the 21st of June, for in- 
stance, it would be 23^ degrees high, and that 
would be its greatest possible altitude. If the 
sun were south of the equator, — that is, between 
September 21 and March 21, — it would be con- 
stant night. When the moon was in north dec- 
lination it would be constantly visible ; as soon 
as it crossed the equator to south declination it 
would disappear. Our observer would have no 
time. He could not, therefore, speak of having 
a good time, or a bad time. He wouldn't have 
any time at all. How could he have? There 
would be nothing to indicate it. The stars would 
not rise in the east and set in the west. He 
would not have any east and west points. He 
could not say it was twelve o'clock when the sun 
was on his meridian. He would lit have any 
meridian. When he started to return to happier 
climes he would not, at first, know whether he 



The Magnetic Pole. 61 



was on his way to China or Peru. He would 
know nothing about the revolution of the earth 
about its axis, for he would n't revolve. He 
would simply face in different directions towards 
space. His north point would be directly over 
his head, and his south point directly under his 
feet. He would be in latitude 90 , and in longi- 
tude o°. Since he had no time, he would have 
no longitude. 

But you may object to my saying that when 
he started to return south he would not know 
what road to take, and ask, " Where is his 
compass?" Why would it not point out the 
north, south, east, and west points to our ob- 
server? Well, I must tell you that the needle 
points to the magnetic pole. Now the magnetic 
pole is not at the north pole of the earth, but is 
in about latitude 70 north and longitude 97 
west. When a ship is in that latitude and longi- 
tude the needle, if freely suspended, will point 
downwards, — towards the nadir, in fact. But 
the compass we use is the mariner's compass. 
The needle is attached to a card and cannot 
point downwards; it is not freely suspended. 
When in high latitudes the card becomes very 
"sluggish," as sailors call it; it does not turn 
upon its pivot and fails to indicate the ship's 
course. This is on account of the " dip " of the 
needle. Arctic navigators find the compass al- 
most useless in high latitudes. Still, I am not 



62 Familiar Talks on Astronomy, etc. 

sure but that a needle freely suspended might 
be of some slight use to our " man at the pole " 
in determining the direction to travel on his 
return south ; but the north point of the needle 
would point south, if it " pointed " at all ; and, 
taking all the circumstances in consideration, he 
would be somewhat in the position of Dickens' 
boy who was in the habit of taking a view of the 
surrounding scenery by standing on his head. 

Let us now transport our observer to the 
equator, and see what the aspect of the heavens 
would be to him. 

The north star (I am supposing it to be at 
the pole, and am disregarding the effect of re- 
fraction) would be on the northern horizon. If 
there were a star just at the south pole of the 
heavens it would be on the southern horizon. 
A star on the equator, — that is, a star of no 
declination, — would rise due east, pass directly 
overhead, and set due west. It would describe 
what astronomers call the prime vertical. All 
the other stars would rise in the east, at all 
points between north and south, and would de- 
scribe vertical circles parallel to the prime ver- 
tical. They would all be above the horizon 
twelve hours, and below it twelve hours. There 
would be no circumpolar stars. 

It would be the same with the sun. At the 
equinoxes the sun would rise due east, pass 



Earth's Velocity in Orbit. 63 

directly overhead, and set due west. At other 
times it would describe a vertical circle either 
north or south of the prime vertical, and would 
at all times of the year be above the horizon 
twelve hours and below it twelve hours. And 
of course the moon would follow the same law. 

You will find it instructive if you will imagine 
yourselves to be in different latitudes, and then 
think out the appearance of the heavens, the 
length of the day, etc. You must first assume 
a certain month and day, of course ; and per- 
haps you are beginning by this time to agree 
with me that astronomy requires much abstract 
thought. 

Shakspeare did not know much about even 
elementary astronomy, as I will point out to 
you some pages farther on ; but he knew enough 
to make Hamlet say : " There are more things 
in heaven and earth, Horatio, than are dreamt 
of in your philosophy." 

If you have any curiosity to know how fast 
we are flying through space around the sun, 
you have only to divide the circumference of 
the earth's orbit by the number of days in a 
year. If you try this, you will find we are 
moving at an average rate of nineteen miles a 
second. And if you wish to know with what 
velocity we are whirling around the earth's axis, 



64 Familiar Talks on Astronomy, etc. 

you have only to divide the circumference of 
the earth by twenty-four, to find the hourly rate ; 
or by 1440, to find the rate per minute. You 
will discover that at the equator the velocity is 
about seventeen miles a minute. Of course here 
in latitude 40 north, we are not revolving with 
such velocity, because it is not so many miles 
round the earth in an east and west direction ; 
but any book on Mensuration will tell you how 
to find the distance round the earth in any lati- 
tude, knowing as we do the circumference at 
the equator. 

What more shall I tell you about the earth? 
We have talked of its shape, size, motions, sea- 
sons, zones, etc. I do not propose to say any- 
thing about its structure, or its atmosphere, 
because books on geology and meteorology 
treat specifically of these subjects. I will, how- 
ever, in a subsequent talk, have something to 
say of the effect of the air on refraction, and 
Columbus's discovery of the trade winds. 



TALK THE FOURTH. 

The Moon. Its shape. Its size. Its Distance from 
the Earth. Its motions. The Moon's Phases. Rule 
for finding the Moon's Age. Earth-shine, or Sec- 
ondary Light. The Moon's Sidereal, and Synodic 
periods. Perigee and Apogee. Librations. 

TN our last talk we confined ourselves to the 
1 Earth. Suppose we now turn our attention 
to its satellite, — our Moon. 

Astronomers tell us that the moon is a round, 
dark, or non-luminous body, shining by the 
reflected light of the sun; 2,153 miles in dia- 
meter, and about 240,000 miles distant from the 
earth. That it is round needs no proof ; we 
see that it is round. That it shines by reflected 
light is shown by its phases. Thales first dis- 
covered this, B. C. 600. Shakspeare says : — 

" The moon 's an arrant thief, 
And her pale fire she snatches from the sun." 

The moon has three motions : it moves 
around the sun; it revolves about the earth; 
it turns upon its axis. How do we know this? 
We know that it moves around the sun because 

5 



66 Familiar Talks on Astronomy, etc. 

it accompanies the earth in its orbit ; we know 
it revolves about the earth by its phases ; we 
know it rotates upon its axis by its always pre- 
senting to us the same face. 

The moon is but 2,153 miles in diameter, 
while the sun is about 866,000 miles in diam- 
eter; yet the moon appears to be of about the 
same size as the sun. Why is this? Because 
it is so very much nearer. The sun is about 93 
millions of miles off, while the moon is but 
about 240 thousands of miles off. The angular 
diameters are about the same (32^) because 
the moon, though so very much smaller, is very 
much nearer. 

Compared to the sun and most of the planets, 
our moon is very insignificant in size. Venus is 
of about the size of the earth, and if brought 
as near to us as the moon, would appear four 
times as large as the moon. But Venus, though 
nearer to us than any other planet, is never less 
than 25 millions of miles distant from the earth. 
Compare this with the moon's distance, and you 
will not wonder that the latter appears so much 
larger and brighter. 

What do we mean by the phases of the 
moon? We refer to the different shapes this 
body assumes. Let us see what causes it to 
appear sometimes as a crescent, and at other 
times round. 



Moon's Phases. 



6? 



You know that the earth, carrying with it the 
moon, revolves about the sun. The moon, too, 
revolves about the earth, though in a much 
'smaller orbit. Now do you not see that the 
moon, in its revolution about the earth, must 
sometimes be between the earth and sun, some- 
times at right angles to a line joining their 
centres, and sometimes it must have the earth 
between the sun and itself? A very simple 




Fig. 3. 

Note. It is to be observed that this diagram, like all others 
in the book, is much exaggerated and out of scale. In point 
of fact, E S is to E A nearly as 400 to I; and the orbit of the 
moon is an ellipse, and not a circle. 



68 Familiar Talks on Astronomy, etc, 

diagram will serve to illustrate this ; and we may 
suppose the earth to be at rest — the phenomenon 
will be the same. 

Let S (Fig. 3) represent the sun ; the point S 
is sufficient to indicate it. Let E be the earth 
in its orbit (only a portion of which is repre- 
sented). It may for our purpose be represented 
by a point. The small circle, A, B, C, D, rep- 
resents the orbit of the moon in its revolution 
around the earth. Let A be the position of the 
moon when it is between the earth and sun ; B 
be its position when it has moved 90 degrees, 
and is at right angles to the line S E, joining the 
centres of the sun and earth ; C be its position 
when it is in opposition to the sun as seen from 
the earth, the earth then being between it and 
the sun; and D its position after it has moved 
90 degrees again. 

Now, when the moon is at A, it is invisible. 1 
It must be. All the light it receives from the 
sun is reflected back in the same direction. Its 
dark side is presented to us, and we do not, of 



1 The two points in the orbit corresponding to new and 
full moon respectively, are called by the common name of 
syzygies; those which are 90 degrees from the sun are called 
quadratures, and the points half way between the syzygies and 
quadratures are called octants. The circle which divides the 
enlightened from the unenlightened hemisphere of the moon is 
called the circle of illumination; that which divides the hemi- 
sphere that is turned towards us from the hemisphere that is 
turned from us, is called the circle of the disk. 



Moon's Phases. 69 

course, see it. It then moves to the eastward of 
the sun, and appears as a crescent. Most of its 
light is reflected back in the direction of the 
sun, but some of it reaches the earth, and as the 
moon is a sphere, it is reflected in the form of a 
crescent. This is what we call the new moon. 
It is to be seen a little after sunset ; and since it 
is in the same direction as the sun, and a little 
to the eastward of it, it follows that it must rise 
in the morning a short time after the sun has 
risen, and must set in the evening a short time 
after the sun has set. It has been above the 
horizon all day, but we have not seen it, on ac- 
count of the sun's light; but as the sun sinks 
below the horizon and its light diminishes, the 
moon is seen as a very delicate crescent, and 
with its round limb towards the sun. 

If we continue to watch it from night to 
night, we shall notice that on the second night 
after the new moon it is farther from the sun, 
and the crescent is larger. Being farther from 
the sun, it sets later in the evening. The third 
night it will be still farther from the sun ; it will 
be larger and brighter and will set later ; and so 
on, until about the seventh night, when it will 
be in the position B in our diagram. One half 
of it is now illuminated (that is, it reflects the 
sun's rays from half its face), and it is said to be 
in its first quarter. It will be on our meridian 
about the time the sun is setting, and we may 



JO Familiar Talks on Astronomy, etc. 

infer that it rose about noon. It has been visible 
all the afternoon, though we probably have not 
observed it. 

Continuing our observations, we shall find the 
moon moving farther and farther from the sun ; 
increasing in size and brilliancy, and setting 
later and later in the night, — until about the 
fourteenth or fifteenth day after the new moon, 
when it will have attained the position C in our 
diagram. It is now directly opposite the sun ; 
it reflects all its rays to us, and it appears round. 
It is now what we call full moon. It rises as 
the sun sets. The full moon must rise as the 
sun sets, because it is opposite to it. We have 
the moon now all night. It rises when the sun 
sets, and sets as the sun rises. 

The next night after full moon we observe 
that it rises about 50 minutes after sunset, 
and that it has very slightly diminished in size ; 
that is, it is not quite a circle. The next night 
again it rises still later, and is still smaller; and 
so on until about the twenty-second day after 
new moon (or about 7J^ days after full moon), 
when we find it rising about midnight. It is 
now in the position D in our diagram. One 
half of it is illuminated, as at B, and it is said to 
be in its last quarter. It is visible now in the 
forenoon, if we look for it. 

From the last quarter it continues to rise 
later and later, and resumes its crescent shape, 



Moon's Phases. yi 

precisely as it appeared between the positions 
A and B. In fact, from full moon we return 
through similar phases, in reversed order, to the 
new moon again. The moon then continues to 
approach the sun until it attains its first po- 
sition, A, in our diagram, when the cycle recom- 
mences. As I have mentioned in our first talk, 
it is not seen for a day or two in every month. 
It is because it is between the earth and sun, 
or so near the sun as to be invisible to the 
naked eye. 

From new moon to full moon it is said to 
wax, and from full moon to new moon to wane. 
From new moon to first quarter, and from last 
quarter to new moon, it is in form a crescent; 
between the first quarter and full moon, and 
between full moon and last quarter, it is gib- 
bous ; and when directly opposite the sun it 
is full. 

After this explanation of the phases of the 
moon you can comprehend why Juliet says to 
Romeo : — 

" O, swear not by the moon, the inconstant moon 
That monthly changes in her circled orb, 
Lest that thy love prove likewise variable." 

The moon was called Selene by the Greeks, 
and Luna by the Romans. 

We have seen that the new moon must rise 
and set with the sun. When it is in its first 



J2 Familiar Talks on Astronomy, etc. 

quarter, it rises about noon; when it is full, it 
rises at sunset; and when it is in its last quarter, 
it rises about midnight. Of course I am speak- 
ing generally as to these times, for the exact 
times depend upon the moon's right ascension 
and declination. But if you will think this out 
until you fully understand it, you will have 
learned a good deal ; as, knowing the moon's 
a g e > y° u can at once make a very close mental 
calculation as to its time of rising. I will give 
you a rule for finding the moon's age. It is a 
good enough rule for practical purposes, and it 
renders you independent of almanacs. I have 
never found it in error more than a day. 



TO FIND THE AGE OF THE MOON. 

To the epact add the day of the month, and 
to this sum add the number of the month from 
March (inclusive). This sum, if less than 30, 
will be the age of the moon. Should the sum 
exceed 30, subtract 30 from it, and the remainder 
will be the moon's age. 

The epact can be found in the Book of Com- 
mon Prayer of the Episcopal Church, and in 
most almanacs. Note that the new epact begins 
in March, not January. I will give you an ex- 
ample to show the working of the rule : required 
the age of the moon Dec. 25, 1885. 



Finding Moon's Age. 73 

Epact for 1885 =14 

Number of the month from March = 10 
Day of the month = 25 

Sum = 49 

Subtract 30 

Moon's age = 19 

This will be four days after full moon, and we 
may infer that the moon will rise about 9 P. M. 

Full moon, you know, must be fourteen or 
fifteen days old, and rises about 6 P. M., or sun- 
set. The exact time of rising depends upon the 
declination of the moon and the latitude of the 
observer. 

Did any of you ever happen to notice that 
our novelists make the moon to rise at any hour 
of the night to suit them ? I am not referring 
to that abominable production called the " nov- 
elette," for of course in it, when the hero and 
heroine have a midnight interview, the full moon 
must be made to appear cotite quHl coute ! But 
I have noticed in the writings of the best Eng- 
lish and American authors such statements as, 
" Shortly after the sun went down the crescent 
moon appeared in the east." Indeed, in a pop- 
ular magazine I read of this remarkable phe- 
nomenon; the time is early in the night, and 
the writer says : " Standing outside the door of 
the church, the young moon, just risen over the 
mountains in the east, they, etc." Dickens him- 
self, in " Barnaby Rudge," says : " It was a fine 



74 Familiar Talks on Astronomy, etc. 

dry night, and the light of a young moon, which 
was then just rising, shed around that peace and 
tranquillity which gives to evening time its most 
delicious charm." 

Do you not see how absurd such a statement 
is? how impossible it is? I could multiply ex- 
amples of such errors if necessary to substantiate 
my position. 1 Even Captain Marryat, in his 
delightful story of " Midshipman Easy," speaks 
of " a crescent-shaped and waning moon being 
seen early in the evening." This cannot be. If 
the moon is crescent-shaped and seen early in 
the evening, it is waxing. A crescent-shaped 
and waning moon can be seen only after mid- 
night. A waning moon seen early in the night 
is always a gibbous moon ; for it must be after 
full moon since it is waning. 

The mere fact that such expressions, so often 
occurring, are not taken notice of by the critics, 
convinces me that I am correct in my belief that 
even elementary astronomy is neglected in the 
education of our youths. Now that I have 

1 Lever, in his description of the advance of the British 
troops from Brussels (Charles O'Malley), speaks of the new 
moon being visible at one o'clock in the morning. 

Rider Haggard, in " King Solomon's Mines," makes the 
new moon rise at sunset. 

And even Coleridge, in his " Ancient Mariner," describing 
the approach of night, says : — 

" Till clomb above the eastern bar 
The horned moon, with one bright star 
Within the nether tip." 



Earth-shine. 7$ 

called your attention to it, I am sure you will 
in the course of your readings come across such 
astounding statements in regard to the appear- 
ance of the moon at critical moments that you 
will be ready to exclaim with Macbeth : — 

" Can such things be, 
And overcome us like a summer's cloud, 
Without our special wonder ? " 

though I will remark, en passant, that I shall 
have something to say concerning even Shak- 
speare's astronomical facts in another place. 

You may have observed that when the new 
moon is first seen, the dark portion of the moon 
is also faintly to be traced with the naked eye. 
If you have never noticed this, do so at the next 
new moon if the weather should be clear. An 
old Scotch poet says : — 

" I saw the new moon late yestreen, 
Wi' the auld moon in her arm." 

Galileo, in 1610, first explained this phenome- 
non. Let us see what the explanation of it is. 

The new moon is seen nearly in a line with 
the sun. The bright crescent is the sun's light 
reflected to us by the moon, as you know. But 
the earth receives light from the sun (and to an 
observer on the moon is full), and this light is 
reflected back to the moon, and is again re- 
flected by the moon back to us, thus causing the 



y6 Familiar Talks on Astronomy, etc. 

entire outline of the moon to be seen, — faintly, 
because the sun's light has suffered a double re- 
flection. As the moon waxes, and moves from 
the sun, this reflected light of the earth becomes 
less and less, and is overpowered by the increas- 
ing light of the moon; consequently the dark 
portion is no longer visible. If you will refer to 
the diagram, page 67, this appears very clearly. 
When the moon is near A, we see that the earth- 
light is reflected back to the moon ; but when 
the moon has moved to B, only a small portion 
reaches it. As a rule the entire moon can be 
seen only for a few nights before and after new 
moon. 

Some astronomers call this earth-shine, and 
others, secondary light. 

The moon revolves about the earth, from west 
to east, in twenty-seven days, seven hours. But, 
as the earth has in that time moved to the east- 
ward in its orbit around the sun, it takes the 
moon a longer time to attain the same relative 
position to the earth and sun ; so that the time 
from new moon to new moon, or from full moon 
to full moon, is twenty-nine days, twelve hours ; 
and this is what we call a lunar month. The 
first period, that is, twenty-seven days, seven 
hours, is the sidereal month. The sidereal month 
is the actual time it takes the moon to revolve 
about the earth, and the lunar month is what 
astronomers call a synodic period. 



Moon s Revolution. jj 

You recollect I told you that the moon re- 
volves upon its axis, and yet we see but one 
side of the moon. Why is this? Since it re- 
volves upon its axis, one would naturally think 
we should see all sides of the moon. Well, it 
revolves upon its axis in exactly the same time 
it takes to make one revolution about the earth ; 
and this is the reason why it always presents the 
same face to us. This is what astronomers say ; 
though it has been disputed, and the point has 
been much discussed. 

When the moon is nearest the earth in her 
revolution, she is said to be in perigee ; and 
when farthest, in apogee. 

As we have seen, the moon presents to us 
always the same face; but in consequence of 
what are called its librations, we see a little over 
its poles and a little around its equatorial edges, 
so that astronomers estimate that we see about 
four-sevenths of the entire surface of the moon. 
Of the remaining surface we know nothing and 
never shall; and if there be inhabitants there, 
they never see the earth. 



TALK THE FIFTH. 

The Moon's angular or apparent Diameter. Its Distance 
from the Earth variable. Parallax. Horizontal Par- 
allax. How it is found. Method of computing the 
Moon's Distance from the Earth, and its Diameter and 
Volume. Light shed by the Moon. Nodes. Physical 
Constitution of the Moon. Lunar Cycle. Influences. 
Tides. Attraction of Gravitation at Surface. 

I HAVE said that the moon is about 240,000 
miles distant from the earth. A good way 
to remember it is to consider it equal to sixty 
radii of the earth, taking the diameter of the 
earth to be eight thousand miles. When we 
measure the moon's angular diameter we find it 
varies considerably from time to time ; ergo, the 
moon's distance from the earth varies. 1 Its least 
distance is 221,000 miles, and its greatest is 
253,000 miles; a difference of 32,000 miles. I 
do not expect you to remember these exact fig- 
ures, but I call your attention to them because 
they have an important bearing upon eclipses, 
which I will explain to you in our talk about 
the sun. 

1 Its orbit being elliptical. 



Moon's Horizontal Parallax. 79 

Let us see how astronomers calculate the 
moon's distance from the earth. It would seem 
to be an abstruse problem, but I think I can 
show you that the method by which it is done 
is not at all difficult to comprehend. I recollect 
in reading Professor Airy's lectures he stated 
that one reason why he was induced to give 
popular lectures was that he had observed that 
persons visiting the Observatory at Greenwich 
always exhibited an air of incredulity when 
told about the magnitudes and distances of the 
heavenly bodies. They seemed to think, with 
Lord Dundreary, " that it was what no fellow 
could find out." Professor Airy was the As- 
tronomer Royal of Great Britain, as you no 
doubt know. 

Now in order to calculate the distance of the 
moon, we have first to find its horizontal paral- 
lax; knowing this, it is very easy to compute 
the distance, — and this applies to all the heav- 
enly bodies ; as soon as we know their parallax, 
we readily find their distances, diameters, and 
volumes. So I must first tell you what parallax 
is. Parallax is the change in the direction of 
an object as viewed from different places ; or, 
it is the angle at the object made by two lines 
drawn from it to the two places. The horizontal 
parallax of a heavenly body is its change of di- 
rection as seen from the centre of the earth and 
the surface of the earth, — the body being on 



80 Familiar Talks on Astronomy, etc. 

the horizon, — or, it is the angle at the object 
subtended by the radius of the earth. 

In the diagram (Fig. 4) suppose the circle 
A B C to represent the earth, O its centre, and 
let A be an observer on its surface. Let M be 
the moon on his horizon A M. The angle A M O 
is the moon's horizontal parallax. 

A - — ^Jif 




Fig. 4. 

Now in order to find the moon's horizontal 
parallax, two observers, one as far north as prac- 
ticable and the other as far south, and both being 




on the same meridian, observe the moon's zenith 
distance when it is on the meridian, and from 
these observations deduce the parallax required. 



Moon's Distance Calculated. 81 

In the diagram (Fig. 5) let O be the centre 
of the earth, PP' its axis, and E Q the equator. 
Let A be an observer in north latitude, and B 
an observer in south latitude. Let M be the 
moon on their meridian. The observer at A 
measures the zenith distance Z A M ; the ob- 
server at B, the zenith distance Z'B M. Know- 
ing these angles we know the angles OAM and 
O B M. Then in the quadrilateral A O B M, we 
know the angles at A and B, and the angle 
A O B ; also the two sides, A O, OB, they being 
radii of the earth. The angle A O B, you ob- 
serve, is the difference of latitude of the two 
observers ; so of course we know it. Now from 
these data we can find the angle A M B. Now 
the angle A M O is what we call the parallax in 
altitude at A, and the angle B M O the parallax 
in altitude at B. Knowing the parallax in alti- 
tude, we can by an easy formula compute the 
horizontal parallax required. 

In the diagram the arc a m b represents an 
arc of the celestial sphere. 

You see that in this method we use the earth 
as a base-line, as it were. And I may as well 
tell you here that the moon is the only heavenly 
body (save only the planet Mars) whose paral- 
lax can be determined in this way, and that, 
because it is so near. The mean horizontal 
parallax of the moon is 57' 3". I say the mean, 
because the distance of the moon varies, as I 
6 



82 Familiar Talks on Astronomy, etc. 

have told you ; and the parallax, you notice, 
depends upon the distance of an object. It has 
nothing to do with its size. 

When we have found the horizontal parallax, 
the distance of the moon is easily computed. 
For, in the right-angled triangle, MAO (Fig. 4), 
we know the angle A M O (the horizontal paral- 
lax just found), and the side A O, the radius 
of the earth ; whence we find O M, the distance 
of the moon from the earth. For example : — 

. _, _ AO 

sine A M = -^-^ , 

or, 

sine AMO X O M = A O ; 
whence, 

OM = AO, cosecant AMO. 
Now, 

AO = 3950 miles, and A M O = 57' 3". 

3950 log. 3.59660 

37' 3" l°g- cosec. 11.78000 

O M = 238,000 log. 5.37660 

This gives us 238,000 miles for the mean distance 
of the moon. 

Now, as soon as we have found the moon's 
distance, we can find its diameter in miles. For 
in the diagram (Fig. 6) let the circle M N 
represent the moon, O its centre, and O M its 
radius ; and suppose E to be an observer on 
the earth's surface. The observer at E measures 
the angular diameter of the moon, that is, the 
angle MEN, the mean value of which he finds 



Moons Diameter and Volume. 



83 



to be 31' 8".8. One half of this is the angular 
semi-diameter, or the angle M E O. Now, in 

M 




Fig. 6. 



the right-angled triangle, E O M, we know E O 
(having just found it), and the angle M E O just 
measured ; whence we find O M. For example : 

OM 



tang. M E O = 



or, 



OM = OE tang. M E O. 

OE = 238,000 miles. log. 5.37660 

M E O = 15' 34"4 log. tang. 7.65589 

OM = 1077.7 miles. log. 3.03249 

1077.7 multiplied by 2, gives us 2055 miles, 
as an approximate diameter for the moon. 

Again, having found the moon's diameter, we 
can easily compute its volume ; for we know 
that the volumes of two spheres are to each 
other as the cubes of their radii. Calling the 
radius of the earth R, and the radius of the 
moon r ; the volume of the earth V, and the 
volume of the moon v, we have 
R 3 : r 3 :: V : v, 
in which proportion we know the first three 
terms. The volume of the moon is about one- 
fiftieth that of the earth. 



84 Familiar Talks on Astronomy ', etc. 

Let us look back for a moment and survey 
the progressive steps by which we have attained 
to a knowledge of the moon's distance, diameter, 
and volume. We first measured a base-line on 
the earth's surface ; then, by triangulation, we 
found the length of one degree of latitude, and 
this gave us the circumference and diameter of 
the earth. These enabled us to calculate the 
volume of the earth. We then used the earth 
for a base-line, and found the moon's horizontal 
parallax. With this, we found the moon's dis- 
tance; having found the distance, we were 
enabled to compute its diameter; and knowing 
the diameter, we found its volume. All this, 
you see, came from the measurement of the 
base-line on the earth's surface. No wonder 
that such pains have been taken to make it as 
accurately as possible, and that the operation 
has been repeated in different parts of the 
world, as I explained to you in our first talk. 

To give you an idea of the light shed by the 
moon, I must tell you that Mr. Lockyer esti- 
mates that it would require 547,513 full moons 
to give as much light as the sun. 1 He says: 
" Now there would not be room for so many in 

1 The earth receives no heat from the moon's rays. Her- 
schel suggested that the heat might be lost in dissipating the 
clouds, which certainly have a tendency to disappear under 
the rays of the full moon. Sailors frequently assert that the 
11 moon will scoff the clouds away." 



Moons Light and Surface. 85 

the half of the sky which is visible to us, as the 
full moon covers 2^-qWo °^ **' nence **• f°hows 
that the light from a sky full of moons would 
not be so bright as sunshine." Think of that ! 

The orbit of the moon is inclined 5 degrees 
to the plane of the ecliptic. The moon, in its 
revolution about the earth, is constantly inter- 
secting the plane of the ecliptic, and the points 
of intersection are called nodes. Thus we have 
the ascending node, and the descending node. 
The moon, too, changes its declination rapidly, 
and frequently crosses the earth's equator in 
the course of a year. 

Let us now see what we know about the sur- 
face of the moon. Our largest telescopes bring 
it within two hundred and forty miles. 1 Not a 
very great distance, you observe. 

We find its surface to be made up of moun- 
tains, valleys, and plains. Most of the mountains 
resemble extinct volcanoes. The surface has 
been accurately mapped, and the mountains, 
volcanoes, and continents named. The heights 
of these volcanoes have even been found ; the 
highest is 27,000 feet high, which you observe 
is relatively higher than our highest mountain. 
In fact, the surface of the moon is much more 
broken up than the surface of the earth. Is it 
not wonderful that astronomers can calculate 

1 The Lick Observatory telescope brings it much nearer. 



86 Familiar Talks on Astronomy, etc. 

the heights of these mountains and volcanoes? 
How do you suppose it is done? They do it 
by means of an instrument called the microme- 
ter, — an instrument used for measuring very 
small angles and spaces, as its name indicates. 
They measure the lengths of the shadows cast 
by these mountains when the sun is rising or 
setting at the moon; and from the lengths of 
these shadows they can calculate the corre- 
sponding heights. And I must tell you that 
some of these astronomers pass their entire 
lives in making observations on the moon alone. 
Photography has lent its aid, and beautiful views 
of the moon have been taken. So one need 
not wonder that so much is known about this 
luminary. 

The moon has no atmosphere. This we know 
by the absence of clouds, and also from the fact 
that when it occults a star, the star disappears 
at once, and does not linger on the edge as it 
would do if there were an atmosphere. The fact 
that the moon has no atmosphere led the great 
humorist, John Phoenix, to say in his book that 
the common expressions, " The moon was gazing 
with an air of benevolence," or, " with an air of 
complacency," were incorrect and objectionable, 
the fact being that the moon had no air at all. 

There are no signs of water at the moon. 
We see, then, that in the absence of air and 
water, it cannot be inhabited. 



Moon's Day. 87 

Moreover, it is conjectured by astronomers 
that, in the absence of an atmosphere to shield 
its surface, or prevent radiation, the surface is, 
in turn, hotter than boiling water, and colder 
than anything we have any idea of. The length 
of its day is 29^ of our days ; so that each por- 
tion of its surface is, in turn, exposed to and 
shielded from the sun for 14^ days. Scientists 
say that the moon may once have been inhab- 
ited, but that it is burnt out. 1 Not a pleasant 
thing for us to contemplate. 

Our telescopes bring the moon within two 
hundred and forty miles. If we continue to 
make them larger, and consequently to bring 
the moon nearer, it is not unreasonable to sup- 
pose that at some future day astronomers may 
be able to discover if there are any signs that it 
was once inhabited. 

The moon, being so much nearer to us than 
any other heavenly body, has naturally been the 
object of curiosity and speculation from time 
immemorial. Dr. Holmes, in his delightful 
" Autocrat at the Breakfast Table," tells us that 
" once upon a time " it was arranged that at a 
given instant every man, woman, and child on 
the surface of the globe should give a loud 
scream, or yell; the idea being to encourage 
the inhabitants of the moon (if there were any) 

1 The latest observations with Lord Rosse's telescope, Pro- 
fessor Langley (I believe) says, make this doubtful. 



5? Famil i ar Talks on Astronomy, etc. 

to give an answering shout When the time 
came, the only persons that screamed were a 
deaf man on one of the Feejee Islands, and an 
old woman in Pekin. All the others, in antici- 
pation of the dreadful noise, had stuffed their 
ears with cotton, and neglected to scream them- 
selves. However true this story may be, it is a 
fact that "once upon a time it was seriously 
proposed by astronomers to erect on the plains 
of Tartar}- an immense structure, so large as to 
attract attention at the moon. It was hoped 
that the people there would, in answer, erect a 
similar one. 

Not long ago I was asked by some very intel- 
ligent and cultured ladies if the moon could ever 
be seen in the daytime. Of course it can. It 
is above the horizon in the daytime during one 
half of its revolution about the earth. It cannot 
be seen for a few cays after the new moon, be- 
cause the sun's light overpowers it; but from 
about the time it is six days old it can be see:; 
from its time of rising, and is visible in the after- 
noon. At the time of full moon it is above the 
horizon only at night 1 In its last quarter it is 
visible all the forenoon. 

You sometimes hear persons speak of a "wet 
moon," or a " dry moon. ig tc its appear- 

1 I am speaking of the temperate zone. Within the 
circle the moon is above the horizon for days when it is at its 
greatest declination, as I have said in chapter iii. 



The Lunar Cycle. 89 

ance at new moon. If the horns of the crescent 
point upwards, so that — as the Indians say — 
"you can hang a powder-horn upon it," it is 
said to be a " dry moon." It is hardly neces- 
sary to say that the position of the crescent 
depends upon the declination of the moon. 

Every nineteen years the phases of the moon 
will recur in precisely the same order and on 
the same days. If, for example, in any year 
the new moon occurs on the 15th of June, it 
will occur again on the 15th of June nineteen 
years after. This is called the lunar cycle, and 
it was known some centuries before Christ. The 
lunar cycle was discovered by Meton, a Greek 
astronomer who lived at Athens in the fifth cen- 
tury before Christ. It was called the Metonic 
cycle. It is still preserved by the churches in 
their computation of Easter, under the name of 
the Golden Number, — so called, because the 
Athenians adopted it about 400 B. c. for the 
regulation of their calendar, and had it inscribed 
in letters of gold on the walls of the temple of 
Minerva. 

Meton observed that two hundred and thirty- 
five revolutions of the moon are very nearly 
nineteen revolutions of the sun, and one com- 
plete revolution of the moon's node. Anthon's 
Classical Dictionary says on this subject: " ' It 
has been suspected,' observes Dr. Hale, ' and 



90 Familiar Talks on Astronomy, etc. 

not without foundation, that the celebrated lunar 
cycle of nineteen years which Meton introduced 
into Greece for the adjustment of their lunar 
year with the solar, was borrowed from the 
ancient Jewish tables. This was the opinion of 
the learned Anatolius, bishop of Laodicea, about 
A. D. 270.' " 

Suppose I speak now of the influences of the 
moon. The most important is its effect upon 
the waters of the earth, producing what we call 
tides. Tides are caused by the attraction of 
both the sun 1 and moon; but the latter being 
so much nearer the earth, its effect is much 
greater. It does not lie within the scope of my 
plan to enter fully upon this subject; but I may 
tell you that, speaking generally, when the moon 
is on the meridian it attracts the water and heaps 
it up, as it were, causing high tide. It pulls the 
earth at the same time towards itself more than 
it does the waters under the earth, thus causing 
a high tide on the other side. Hence there 
must be two high tides in every lunar day (24 
hours, 54 minutes), and also two low tides. 
Theoretically, it should be high water at a place 
when the moon is on the meridian of that place ; 

1 Shakspeare says : " The sun 's a thief, and with his great 
attraction robs the vast sea." He also says : " For the fortune 
of us that are the moon's men doth ebb and flow like the sea ; 
being governed, as the sea is, by the ?noon ! " — Henry IV. 

Query : How did Shakspeare know this ? 



Moon's Influences. 91 

but tides, like the winds, are very much modified 
by local causes. Since it is the moon that prin- 
cipally causes the tides, high water at any place 
occurs about fifty minutes later from day to 
day, just as the moon rises later by that time. 
You must not confound currents with the tides. 
We find currents in every ocean ; the Gulf 
Stream and the Japanese current are notable 
examples. We are not always able to explain 
the cause of the ocean currents ; we only know 
that they exist, and observation tells us their 
velocity. I suppose you know what is meant 
by a town being at the head of tide water on a 
river ; but if not, I will tell you that the tides of 
the ocean flow up all rivers a certain distance, 
and then stop. This marks the head of tide 
water; below this, the tide ebbs and flows. 
Above this point the waters, like the waters of 
the historical Tombigbee, always run down. 
Perhaps you may remember that Lander, who 
first descended the Niger River, looked eagerly 
for signs of " tide ; " and in later days, Strain, 
who crossed the Isthmus of Darien and who de- 
scended the Chuquinaque to the Pacific Ocean, 
— half-starved and floating on a raft, — with 
what joy he welcomed the signs of " tide " and 
salt water. But this en passant. 

It is popularly believed that the moon affects 
the weather, the crops, meat, and fish. It is 
even said that persons sleeping in its full light 



92 Familiar Talks on Astronomy, etc. 

will have their features drawn awry. None of 
these things are true. Arago, a French astron- 
omer who examined the records for many years 
back, says there is no evidence to show that the 
moon affects the weather ; and I have seen half 
the crew of a Line-of-Battle ship asleep under 
the light of a full moon, not once, but many 
times, and not a man of them ever " made a 
face." It used to be thought that madmen be- 
came more violent under a full moon ; indeed, 
we get the word lunatic from luna, the moon. 
Thus Milton says, in " Paradise Lost:" — 

" Moping melancholy, 
And moon-struck madness." 

I am inclined to believe, however, that madmen, 
like other people, are subject to bright influences. 

One thing more I will speak of before I con- 
clude this long talk. The moon being much 
smaller than the earth (its mass being about -fa 
of the earth), the attraction of gravitation at its 
surface is much less than the earth's at its sur- 
face. It is calculated that a man there could 
jump six times as high as on the earth. So you 
see that if any of my young readers were trans- 
ported to the moon, and should there attempt a 
" german " or quadrille, they would find them- 
selves dancing as Queen Elizabeth is said, by 
Lord Melville, to have danced, — that is, " high 
and disposedly." 



TALK THE SIXTH. 

The Sun. Its Shape. Size. Motion. Distance. Rela- 
tive Distances of the Planets from the Sun. Transits 
of Venus. Sun's Parallax. How determined. Method 
of finding the Sun's Distance, Diameter, and Volume. 
Disk. Photosphere. Point at which Sun rises. 

TJAVING finished our talks about the earth 
and moon, let us now turn our attention to 
our great luminary, the Sun, — the centre of our 
system. What do we know about it? 

Astronomers have discovered that it is a 
round, incandescent mass, about 866,000 miles 
in diameter, and that it turns upon its axis once 
in from 25 to 28 days. It is distant from the 
earth about 93,000,000 miles. 

Let us first see how its distance is deter- 
mined ; and you will appreciate the importance 
of this problem when I tell you that upon its 
determination depend the distances of all the 
planets (save only Mars) from the sun, and 
from the earth. And I may say, too, their di- 
ameters, volumes, and masses ; for we have seen 
that these are derived from a knowledge of their 
distances from the earth. 



94 Familiar Talks on Astronomy, etc. 

Before the distance of the sun was known, 
astronomers knew the relative distances of the 
earth and planets from the sun, but not their 
real distances. For example: they knew that 
Venus was seven-tenths as far from the sun as 
the earth is, and Mars about one and six-tenths 
as far. I will explain to you farther on how 
they found this out. But you see that with the 
knowledge they had, as soon as the sun's real 
distance became known, the others followed. 

As in the case of the moon, the sun's distance 
is readily calculated as soon as we can discover 
its parallax. The parallax of the sun is the 
angle subtended by the earth's radius as seen 
from the sun. I only repeat what I told you in 
our last talk; but I wish you to fully under- 
stand the meaning of parallax. 

The planet Venus sometimes passes directly 
between the earth and the sun. It is projected 
on the face of the sun as a round, black spot. 
This is called a transit of Venus. Unfortunately 
these transits occur very rarely, the intervals 
between them being 8, 105, 8, 122 years, and 
so on. 

In 1 69 1 the English astronomer, Halley, 
pointed out that the parallax of the sun could 
be determined by these transits, and earnestly 
requested astronomers to take advantage of the 
transit to occur in 1761, which he, of course, 
could not hope to live to see. The first observ- 



Sun's Parallax. 95 

ations were made in 1761, and again in 1769. 
These observations have to be made at places 
far apart on the earth's surface, and one of the 
objects of the last voyage of Captain Cook (the 
great English navigator) was to observe the 
transit of 1769, which he did at the Society 
islands, in the Pacific ocean. 

The method by which the parallax of the sun 
is deduced from these observations, is too ab- 
struse to be explained here. No doubt many 
of those employed in making the observations 
and calculations spent years in the preparation 
for it. We will simply accept the fact that the 
parallax of the sun can be determined in this 
way. 

The observations of 1769 gave for the par- 
allax 8">6 -f-. Think of this for a moment. The 
sun is so distant that the radius of the earth 
(about four thousand miles) subtends at the 
sun only an angle of &".6. Why, we could not 
pretend to draw this on a scale ; the angle 
would not be the thickness of a hair. 

The sun's radius subtends at the earth an 
angle of about 16'; this is small enough, but it 
is much greater than the angle subtended by 
the earth's radius at the sun, because the sun is 
very much larger than the earth. Compare 
them: The sun is 866,000 miles in diameter, 
and the earth barely 8,000. The angular di- 
ameter of the sun is about 32'; the angular 



g6 Familial' Talks on Astronomy, etc. 

diameter of the earth (measured at the sun) is 
about iy". 

A transit of Venus occurred in 1874, and 
another in 1882; and both were observed with 
great care, for there will not be another one 
until 2004, — 115 years hence. Expeditions 
were sent by the European and American na- 
tions to different places. I think there were as 
many in all as forty-six. The Americans had 
stations at Chatham island, Kerguelen island, 
and other places. The observations have not 
yet been worked out ; so the new determination 
of the sun's parallax has not been published. 
Although the principle is quite easy to under- 
stand, the calculations are very complicated. 
Our Grand Observatory is the earth, and it is in 
motion. Do you not see how this must compli- 
cate all celestial observations? Photography 
has lent its aid to assist in the observations of 
these transits, and views were taken at the 
different stations at the last transit. 

The result, when published, will not probably 
differ much from the parallax now accepted, 
say 8'.8i. I believe astronomers only expect to 
make a change in the third figure, — that is, in 
the hundredth part of a second. We are inter- 
ested in the result for more reasons than one. 
A change in the sun's parallax involves a 
change in its distance ; and that, again, involves 
a change in the distances of the planets. But 



Sim's Distance Found. 97 

suppose our astronomers should find the sun's 
parallax to be considerably increased? What 
would that indicate? Why, that the earth is 
much neare'r the sun than in 1769. Now, if the 
earth should once begin to approach the sun, 
it would move with a greatly accelerating ve- 
locity, — since the law of gravitation (discovered 
by Sir Isaac Newton in 1682) shows that the 
attraction of gravitation decreases as the square 
of the distance increases, and the reverse \ — and it 
would soon fall into the sun, and be consumed. 

In point of fact, however, if we should find 
a considerable difference in the parallax, we 
should be more inclined to attribute it to the 
imperfection of the instruments used in the 
observations of 1769; for we know that the earth 
is not approaching the sun, — except that it is 
nearer to it at times than at others, as it should 
be, its orbit being an ellipse with the sun in one 
of the foci. 

How do we know that the earth is not falling 
into the sun? Simply because the sun's angular 
diameter remains the same. We do not want 
any better proof than this. 

There is another method by which the sun's 
distance can be found, and that is by first find- 
ing the distance of the planet Mars from the 
earth. Two observers — one at Greenwich, 
the other at the Cape of Good Hope — made 
7 



98 Familiar Talks on Astronomy, etc. 

precisely the same observations of Mars, as I 
have described in the case of the moon, and 
found its parallax and distance from the earth. 
When Mars is in opposition (as it was when the 
observations were made), its distance from the 
earth is one third of the distance of the sun 
from the earth. Hence, having found its dis- 
tance, we multiply it by 3, and get the distance 
of the sun from the earth. 

This method is not considered so accurate as 
the method of finding the distance by a transit 
of Venus, but it gives for the sun's distance 
91^2 millions of miles, — a close approximation. 

We cannot find the parallax of the sun by the 
method we use in finding the parallax of the 
moon or Mars, because it is so far off. The 
entire diameter of the earth would not give us a 
base-line long enough. 

Having found the sun's parallax, we find its 
distance, diameter, and volume, precisely as we 
do in the case of the moon. I have given you 
its distance and diameter; its volume is about 
1,300,000 times that of the earth. 

The sun turns upon its axis once in about 
25 days. How in the world did astronomers 
find this out? Let us see. The disk of a 
heavenly body is its face as it appears projected 
on the sky. We see on the sun's disk certain 



Sim's Heat. 99 

spots. Galileo first called attention to them in 
161 1. I am sure you all must have noticed that 
the papers frequently speak of there being spots 
on the sun. 

Astronomers carefully observe these spots, 
and notice that they make their appearance on 
one edge of the sun's disk, and that they take 
about I2j£ days to traverse it. Now, as the 
spots preserve their relative positions to each 
other, we do not suppose them to move across 
the face of the sun, but rather that the sun re- 
volves and carries them with it. There is some 
uncertainty as to the exact time of the sun's 
rotation, but it is between 25 and 28 days. 

Is the sun inhabited? This seems a foolish 
question to ask, does it not? If it is really an 
incandescent globe, of course it is not; but if 
the incandescence is confined to its photosphere 
(as some scientists think), and the surface of its 
globe is protected by a dense atmosphere, it 
may be inhabited. 1 

We have no evidence that the sun has lost 
any of its heat from the beginning of the world. 
Where, then, does it get its supply of fuel? We 
do not know, and probably never will know. 
The question belongs to what we may call 
speculative astronomy. Many such questions 

1 Hardly any astronomers think so, however. 



ioo Familiar Talks on Astronomy, etc. 

arise, and some astronomers spend their lives in 
attempting to find the explanation of them. 

Theoretical astronomy is an exact science. 
We can calculate the positions of the heavenly 
bodies, their dimensions, their motions, predict 
eclipses and occultations, find the latitude and 
longitude, etc., with absolute accuracy; but such 
questions as the nebular hypothesis, or how the 
stars and planets were first formed ; the physi- 
cal constitution of the sun and planets, etc., 
are for the present speculative. We may 
safely leave them to the great astronomers of 
the world. 

The earth, as seen from the sun, would appear 
as a star of the fifth or sixth magnitude. Venus 
which is about the size of the earth, appears to 
us as a very bright star. It is about thirty-six 
million miles from us when in conjunction ; re- 
move it to a distance of ninety-two million miles, 
and it would appear to us as the earth appears 
to the sun ; that is, as a very insignificant star. 
The sun itself, brilliant as it appears to us, sinks 
into insignificance in comparison to the fixed 
stars, which you know are themselves suns, and 
probably each one the centre of a system, just 
as our sun is. Why, do you know that if the 
sun were removed to the distance of the nearest 
star (alpha Centauri), it would appear to us as 



Elements in the Sun. ioi 

a star of the second magnitude ! It is almost 
impossible to comprehend such a statement. 

The sun's bright surface is called the photo- 
sphere. The photosphere is simply what we 
see of the sun ; whether it be the body of the 
sun, or simply its atmosphere or clouds. Do 
we know any of the materials of this photo- 
sphere? Yes; we have discovered them by 
means of the spectroscope. We have discovered 
that certain substances are burning in the sun 
and stars, and we find them to be nearly the 
same in all. These observations, known as the 
" Spectrum Analysis," tell us that the elements 
in the sun are sodium, iron, magnesium, barium, 
copper, zinc, calcium, chromium, nickel, and 
others. In the stars, sodium, magnesium, iron, 
and perhaps hydrogen and barium. Our knowl- 
edge in this direction is constantly increasing, 
many astronomers giving their entire attention 
to this subject. 

In the case of the moon, which has no atmos- 
phere, we view it through a telescope and dis- 
cover land, volcanoes, beds of oceans (dry), etc. 
It has no photosphere. 

You remember that in our first talk I prom- 
ised to say something more in relation to the 
exact point in the east at which the sun rises at 
different seasons of the year. It never rises at 
precisely the same point for two successive days. 



102 Familiar Talks on Astronomy, etc. 

You must have observed that in summer it rises 
well up towards the north, and in winter down 
towards the south. When it crosses the equator 
it rises due east to an observer, it matters not 
what latitude he may be in. On no other days 
of the year does it rise due east. After the 
vernal equinox, and until the autumnal equinox, 
it rises north of east and sets north of west to 
all observers in north latitude ; and the farther 
north the observer, the farther to the north does 
the sun rise and set. In winter, that is, our win- 
ter, the sun rises south of east and sets south of 
west. 

Shakspeare did not know this ; for in " Julius 
Caesar," in a dispute as to the east point, Casca 
says, — 

" You shall confess that you are both deceived. 
Here, as I point my sword, the sun arises; 
Which is a great way growing on the south, 
Weighing the youthful season of the year, 
Some two months hence, up higher toward the north 
He first presents his fire ; and the high east 
Stands, as the Capitol, directly here." 

Casca was in error. As the time was the ides 
of March, that is, the 15th day of March, the 
sun rose only two degrees south of the east point, 
or we may call it directly or due east. " Some 
two months hence," that is, May 15, it would 
rise to an observer at Rome about east-north- 



Shakspeare 's Astronomy. 103 

east; though Casca evidently meant to say that 
it will then, and not till then, rise due east. 

While upon this subject I will call to your 
notice that Shakspeare pays little attention to 
astronomical facts. For example, in " Midsum- 
mer Night's Dream," at the opening of the play, 
Theseus says to Hippolyta, — 

" Four happy days bring in 
Another moon ; but oh ! methinks how slow 
This old moon wanes, etc.," — 

referring to their approaching nuptials. Yet 
only a night or two after, the clowns — who are 
preparing to act a piece in celebration of the 
marriage — have a discussion at the rehearsal 
as to whether there will be a moon that night. 
Thus, — 

Snug. Doth the moon shine that night we play our play ? 
Bottom. A calendar ! a calendar ! look in the almanac ; 

find out moon-shine. 
Quince. Yes, it doth shine that night. 

and we know that one of them acted moonshine 
accordingly. Either Theseus was mistaken, or 
the almanac was incorrect, certainly. 

It shows how little attention the literary men 
of the last century paid to the science of as- 
tronomy; for Steevens, Farmer, Malone, Dr. 
Johnson, and other commentators, never (so far 
as I have observed) take any notice of these 



104 Familiar Talks on Astronomy, etc. 

inaccuracies, though the proper reading of 
Shakspeare's plays has been the subject of 
controversy ever since they were first published. 
Volumes have been written on the subject. 

I have already called your attention to the 
fact that the authors and critics of the present 
day are guilty of the same oversight. 



TALK THE SEVENTH. 

Eclipses. Occupations. A Solar Eclipse. Total, An- 
nular, and Partial Eclipses. Digits. Lunar Eclipse. 
Inclination of Moon's Orbit to Plane of the Ecliptic. 
Number of Eclipses in a Year. Cycle of Eclipses. 
Sun's Influences. Its Light and Heat. 

]\]OW that we know something about the sun 
and moon, suppose we turn our attention 
to the eclipses of these bodies. 

When the moon passes directly between the 
earth and sun, the latter is said to be eclipsed ; 
and when the earth is between the sun and the 
moon, the moon is eclipsed. There is a differ- 
ence between an occultation and an eclipse, 
though we are apt to consider them synony- 
mous terms. Eclipse is from the Greek, and 
means a disappearance ; occultation is from oc- 
ciritare, to hide. When the moon is eclipsed it 
is in the shadow cast by the earth, and it dis- 
appears. When a star is hidden from sight in 
consequence of the moon passing between it 
and the earth (a thing which happens very fre- 
quently) it is called an occultation. Thus, we 
speak of the occultations of Jupiter's satellites, 



106 Familiar Talks on Astronojny, etc. 

which are caused by Jupiter passing in front of, 
and hiding them from our view. When the 
satellites pass into the shadow cast by Jupiter, 
they are eclipsed. I suppose we may say that 
an occultation is an eclipse, but an eclipse is not 
an occultation. 

Let us first consider an eclipse of the sun, or 
a solar eclipse. When the moon is directly be- 
tween the earth and the sun, that is, you observe, 
at the time of new moon, we have an eclipse of 
the sun. It may be total, annular, or partial. 

If the centre of the moon passes directly over 
the centre of the sun, and if, moreover, the 
moon is in that part of its orbit nearest the 
earth, it produces a total eclipse. The shadow 
cast by the moon (which you observe is conical 
in shape) reaches the earth, though it is never 
very large, its diameter averaging about 150 
miles. But to all observers in this shadow the 
sun entirely disappears, and it is eclipsed. A 
total eclipse is very rare, and never lasts over 
eight minutes at any one place. 

Now, suppose the centre of the moon to pass 
directly over the centre of the sun, but let the 
moon be in that part of its orbit farthest from 
the earth. In this case the shadow cast by the 
moon does not quite reach the earth, and an 
observer on the earth's surface, situated in a line 
with the centres of the two bodies, will witness 



Solar and Lunar Eclipses, 107 

that uncommon phenomenon called an annular 
eclipse. The moon does not quite cover the 
face of the sun ; its angular diameter is a little 
less than the sun's ; and we see a bright narrow 
ring of light encircling the dark body of the 
moon, — hence annular, from annulus, a ring. 

Just as the moon would appear to us if we 
should hold a silver dollar between us and it. 
When we hold the coin close to the eye, the 
moon is not seen ; but if we hold it farther and 
farther off, keeping its centre over the centre of 
the moon, we can finally hold it where it does 
not entirely cover it, but leaves a bright ring 
visible. An annular eclipse occurs very, very 
rarely. 

Most of the eclipses of the sun are what we 
call partial. The centre of the moon does not 
pass directly over the centre of the sun, and 
consequently only a portion of the sun's disk is 
obscured. For the sake of distinction astron- 
omers imagine the diameter of the sun to be 
divided into twelve equal parts, called digits, 
and the number of digits obscured is stated. 
Thus, an eclipse of nine digits would indicate 
that three-fourths of the sun's face is obscured ; 
and this applies also to the moon in a lunar 
eclipse. 

When the earth is between the sun and the 
moon, and the latter passes into the shadow cast 



108 Familiar Talks on Astronomy, etc. 

by the earth, we have a lunar eclipse, or an 
eclipse of the moon. It may be total, or partial, 
and you observe can happen only at full moon. 
If the moon is near, but not at, a node, we have 
a partial eclipse. When the moon passes 
through the centre of the shadow, it is totally 
eclipsed. But even in this case the moon's disk 
is scarcely ever wholly obscured. The sun's 
light is bent by the earth's atmosphere, by what 
we call refraction, towards the moon, and some- 
times tinges it with a ruddy color. In an 
eclipse of the moon the shadow of the earth as 
cast upon the moon is seen to be circular, which 
is one of the proofs that the earth is round. 

It is to be observed that an eclipse of the 
moon is visible to the whole side of the earth 
turned away from the sun, because the shadow 
cast by the earth is so large; whereas, as we 
have seen, an eclipse of the sun is visible over 
a small area, because the shadow cast by the 
moon is small. 

Now you will very naturally ask why we do 
not have a solar eclipse at every new moon, and 
a lunar eclipse at every full moon. If the orbit 
of the moon coincided with the plane of the 
ecliptic, we would have these eclipses every 
month. But it does not. It is inclined to the 
ecliptic 5 , and consequently the moon very 
rarely passes exactly between the earth and 
sun, nor does it often pass through the earth's 



Cycle of Eclipses. 109 

shadow. It generally passes above or below the 
sun, and above or below the earth's shadow. 

In fact, the greatest number of eclipses that 
can occur in any one year is seven, and the 
least, two. Astronomers can calculate them 
with the utmost accuracy for years ahead. The 
Chinese learned to do so centuries ago ; and it 
is said that Thales, about 585 B.C., was able to 
predict one. 

You may remember that Columbus, during 
his fourth voyage in 1504, was wrecked on the 
island of Jamaica, and was dependent upon the 
natives for a supply of provisions. The Indians 
becoming negligent, or refusing to continue the 
supply, Columbus, who knew that an eclipse of 
the moon was about to take place, called them 
together, and told them the Great Spirit was 
displeased with them, and on a certain night 
would hide his face. When the moon became 
dark, the Indians, convinced of the truth of his 
words, hastened to bring supplies of food as 
usual. 1 

Just as we have seen that every nineteen years 
the moon's phases will recur in the same order, 
— which period of nineteen years we call the 
lunar cycle, — so will eclipses recur in precisely 

1 This anecdote is relatqd by Irving in his " Life of Colum- 
bus." He quotes Las Casas as an authority. It should betaken 
cum grano salts ; for, I believe, astronomers have calculated 
that no eclipse of the moon happened at the date given. 



HO Familiar Talks on Astronomy, etc. 

the same order every eighteen years and eleven 
days. This is called the cycle of eclipses, and 
it was known to the ancient Chaldeans and 
Greeks under the name of Saws ; and by its 
means eclipses were predicted before astronomy 
had made much progress. 

Let us now glance at some of the benign in- 
fluences of the sun. We know that our earth 
is lit up by its beams and warmed by its heat. 
But this is not all. Mr. Norman Lockyer says, 
in his astronomy : — 

" There is something else besides light and heat in 
the sun's rays, and to this something we owe the fact 
that the earth is clad with verdure ; that in the tropics, 
where the sun shines always in its might, vegetable life 
is most luxuriant, and that with us the spring-time, 
when the sun regains its power, is marked by a new 
birth of flowers. 

"There comes from the sun, besides its light and 
heat, chemical force, which separates carbon from oxy- 
gen, and turns the gas which, were it to accumulate, 
would kill all men and animals, into the life of plants. 
Thus, then, does the sun build up the vegetable 
world." 

Again, we are apt to think that the earth re- 
ceives all of the light and heat radiated by the 
sun. Mr. Lockyer tells us that we receive less 
than one billionth part of it; and further, that 
all the planets together receive but one two hun- 



The Sun's Heat. in 

dred and twenty-seven millionth part of the solar 
light and heat. He estimates that the whole 
heat of the sun collected on a mass of ice as 
large as the earth would be sufficient to melt it 
in two minutes, to boil the water thus produced 
in two minutes more, and to turn it all into 
steam in a quarter of an hour from the time it 
was first applied. 



TALK THE EIGHTH. 

Recapitulation. The Planets. Those known to the An- 
cients. Discovery of Uranus and Neptune. Inferior 
and Superior Planets. Satellites. Discovery of the 
Satellites of Jupiter and Mars. Speculations of Bishop 
Wilkins and others concerning the Moon. The Ele- 
phant in the Moon. Mercury : its Size, Distance from 
Sun, and Motions. Inferior and Superior Conjunc- 
tions. Quadratures. Phases. Transits. Venus : its 
Size, Distance from Sun, and Motions. Phases. 
Transits. Mars : its Size, Distance from Sun, and 
Motions. Opposition and Conjunction. Jupiter, Sat- 
urn, Uranus, and Neptune. Bode's Law. The Satel- 
lites of Jupiter. 

BEFORE taking up the subject of the planets, 
let us go back again and see what we have 
learned thus far in regard to the motions, dimen- 
sions, distances, and volumes of the earth, moon, 
and sun. 

We have learned that the earth is an oblate 
spheroid, turning upon its axis from west to east 
once in 23 hrs., 56 min., 4 seconds, and moving 
in an elliptical orbit around the sun once in 
about 365^ days. By measuring a base-line 
on its surface, we found the length of one degree 



The Solar System. 113 

of latitude, and from that its circumference, 
diameter, and volume. Having found the size 
of the earth, we next found the horizontal par- 
allax of the moon, from which we calculated its 
distance, diameter, and volume. We found the 
moon had three motions, and that in conse- 
quence of one of them (its revolution about the 
earth), and the fact that it shines by reflected 
light, it exhibited phases. In the case of the 
sun, we discovered the time of its rotation by 
observations on its spots ; and by a transit of 
Venus we found its parallax, and hence its dis- 
tance, diameter, and volume. The size of the 
earth, the distance and size of the moon and 
sun, all depended upon the measurement of one 
small base-line on the earth's surface. 

Now let us turn our attention to the planets. 
Our solar system comprehends the sun, as a 
centre, and the planets Mercury, Venus, the 
Earth, Mars, Jupiter, Saturn, Uranus, and Nep- 
tune. I will speak of the asteroids in another 
place. 

The sun is supposed to be at rest; and all 
the planets revolve about it, from west to east, 
in elliptical orbits. They also rotate upon their 
axes, from west to east, and all are dark bodies 
and shine by reflected light. 

The planets Mercury, Venus, Mars, Jupiter, 
and Saturn, were known and named by the an- 



114 Familiar Talks on Astronomy, etc. 

cients. Uranus was discovered in 1781 by Sir 
William Herschel, and Neptune in 1846 by Dr. 
Galle of Berlin, who had previously been in- 
structed by Le Verrier where to look for it. 
The discovery of this planet is justly considered 
one of the greatest triumphs of science. Owing 
to certain irregular motions of the planet Uranus 
in its orbit, — perturbations, as they are called, 
— astronomers were led to suppose that they 
might be occasioned by the existence of another 
planet outside of its orbit. Under this suppo- 
sition alone, Adams, an English astronomer, and 
Le Verrier, a French astronomer, actually cal- 
culated where this supposititious planet should 
be. Singular to say, neither knew of the other 
being engaged in the same work ; yet their cal- 
culations agreed very nearly, and the result was 
the discovery of the planet Neptune. 

Mercury and Venus are between the earth 
and the sun, and are called inferior planets ; the 
others are outside the earth's orbit, and are 
called superior planets. This has no reference 
to their size. The planets are distinguished 
as primaries, and their satellites are termed 
secondaries. 

Most of the planets have satellites or moons. 
The Earth has one, Mars two, Jupiter four, Sat- 
urn eight, Uranus four, and Neptune probably 
one. These satellites, excepting the moon, were 
not known to the ancients, because they cannot 



The Satellites of Mars. 1 1 5 

be seen with the naked eye. They were not 
discovered until the telescope was invented. 
Galileo, who first used it, immediately discov- 
ered the moons of Jupiter. His telescope was 
a very rude one, but the moons of Jupiter re- 
quire but a small magnifying power to become 
visible. As telescopes were improved and made 
more powerful, the moons of Saturn and Uranus 
were discovered ; but, strange to say, the moons 
of Mars were not seen until 1877, — only a few 
years ago. They were discovered by Professor 
A. Hall of the United States Navy, at the Wash- 
ington Observatory. 

I presume you have all read " Gulliver's Trav- 
els," — a fictitious work written by Dean Swift, 
in the reign of Queen Anne. One of the travels 
is called " A Voyage to Laputa." It was doubt- 
less intended as a satire on the astronomers of 
the day. Well, Gulliver says of the astronomers 
on the imaginary island of Laputa : " They have 
likewise discovered two lesser stars or satellites, 
which revolve about Mars, whereof the inner- 
most is distant from the centre of the primary 
planet exactly three of his diameters, and the 
outermost five." Rather a remarkable predic- 
tion in a work of fiction to be verified ; but Swift 
is not the only writer who, in a freak of fancy, 
has anticipated the discoveries of Science. 

Soon after the invention of the telescope, 
scientific men looked for great discoveries, par- 



n6 Familiar Talks on Astronomy, etc. 

ticularly in the direction of the moon. The 
Royal Society of England was founded about 
this time, and the wits of the age were accus- 
tomed to ridicule its labors. Among its founders 
was Bishop Wilkins, who about the year 1650 
published a work entitled " The Discovery of a 
New World," alluding to the moon. If the sci- 
entists of the day indulged in as wild specula- 
tions as the Bishop, one cannot wonder that 
they were ridiculed. I will give a few extracts 
from his work to illustrate what I said upon the 
subject in our talks about the moon. In his 
discourse to prove that the " moon may be an 
habitable world," he says, — 

" 'T is the opinion of Kepler that as soon as the Art 
of flying is found out, some of their Nation will make 
one of the first Colonies that shall transplant into that 
other World. I suppose his appropriating this Pre- 
heminence to his own Countrymen may arise from an 
over-partial Affection to them. But yet thus far I 
agree with him, that whenever that Art is invented, 
or any other, whereby a Man may be conveyed some 
twenty Miles high, or thereabout, then 'tis not alto- 
gether improbable that some or other may be successful 
in this attempt." 

Speaking of the "Gibbosities" of the moon, 
he says, — 

" Now if you should ask a reason why there should 
be such a multitude of these in that Planet, the same 
Kepler shall jest you out an Answer. Supposing (saith 



Bishop Wilkins Speculations. 1 1 7 

he) that those Inhabitants are bigger than any of us, in 
the same proportion as their days are longer than ours, 
— viz. by fifteen Times, — it may be, for want of Stones 
to erect such vast Houses as were requisite for their 
Bodies, they are fain to dig great round Hollows in the 
Earth, where they may both procure Water for their 
Thirst, and turning about with the Shade, may avoid 
those great Heats which otherwise they would be liable 
unto." 

And again, — 

" Kepler calls this World [the Moon] by the Name 
of Levania, from a Hebrew word which signifies the 
Moon, and our Earth by the Name of Volva, a vol- 
vendo, because it does by Reason of its diurnal Revo- 
lution appear unto them constantly to turn round ; and 
therefore he stiles those, who live in that Hemisphere 
which is towards us, by the Title of Subvolvani, be- 
cause they enjoy the Sight of this Earth, and the others 
Privolvani, quia sunt privati conspectit volvce, because 
they are deprived of this Privilege." 

It was to hold up to ridicule such writings as 
the above that Butler (the author of " Hudi- 
bras") wrote his satire entitled "The Elephant 
in the Moon," — the "elephant" being nothing 
more nor less than a mouse which had gotten 
in between the eye-piece and the object-glass of 
the telescope. This satire appeared somewhere 
about 1665-70. In Sprat's " History of the 
Royal Society" appeared a " Relatio7i of the 
Pico TenerifTe, received from some considerable 



1 1 8 Familiar Talks on Astronomy ', etc. 

Merchants, and Men worthy of Credit, who went 
to the Top of it" in which it was stated that the 
inhabitants of the Canary Islands whistle so loud 
as to be heard five miles off; " and that to be in 
the same room with them when they whistle, 
were enough to endanger breaking the Tympa- 
num of the Ear." Butler says in his satire, — 

" Or Men that used to whistle loud enough 
To be heard by others plainly five Miles off, 
Cause all the rest, we own, and have avow'd 
To be believed as desperately loud." 

In this day I presume a whistle can be heard 
quite five miles, through a telephone. 

MERCURY. 

Let us commence with Mercury, the nearest 
planet to the sun. 

Its diameter is about 3,000 miles, and its mean 
distance from the sun about 56,000,000 miles; 
it turns upon its axis once in 24 hrs., 5 min., 1 
and it makes one revolution about the sun in 88 
days. Its day, then, is about the length of ours, 
and its year is about one fourth as long as ours. 
Its volume is one nineteenth that of the earth. 

In the diagram (Fig. 7) let S be the sun, E 

the earth, and M, IVf, M", M'", . be Mercury in 

four different positions in its orbit. Since the 

earth and Mercury move around the sun with 

1 See note, page 137. 



The Planet Mercury. 



119 



different velocities, they will have all possible 
relative positions with respect to each other ; so 
we may, for the purpose of illustration, suppose 
the earth to be at rest in its orbit. Let EE' 
represent the orbit of the earth, and M, M', M", 
the orbit of Mercury. 




Fig. 7. 



We see from this diagram that Mercury can 
never be in opposition to the sun ; that is, seen 
in a line directly opposite the sun. Hence it 
can never be on the meridian at midnight, nor 
can it be above the horizon at midnight. 1 It can 
go, indeed, but twenty-nine degrees from the 
sun, and consequently it is rarely to be seen 

1 Pope says : 

" And Venus sets ere Mercury can rise " — 
which is an absurdity. 



120 Familiar Talks on Astronomy, etc, 

with the naked eye. It is generally so near the 
sun that the sun's light overpowers it. 

When Mercury is at M, it is between the 
earth and sun, and is said to be in inferior con- 
junction. When it is at M", the sun is between 
it and the earth, and it is said to be in superior 
conjunction. When in either of these two posi- 
tions it must rise and set with the sun, and it is 
not visible. You see this at once ; since it is in 
a line with the sun, it must rise and set with it. 

The positions M', M'", represent its points 
of greatest eastern and western elongations, or 
quadratures. Its greatest angular distance from 
the sun is represented by the angle M' E S, or 
M //r E S, and it can never exceed 29 degrees. 
When Mercury is west of the sun it will rise 
before it, and will appear (if it can be seen at 
all with the naked eye) as a morning star. 
When it is east of the sun, it will set after the 
sun, and will be an evening star. 

You perceive from the diagram that its dis- 
tance from the earth varies very much. It is 
nearest to us at M (inferior conjunction), and 
farthest at M /; (superior conjunction). What is 
the difference between these two distances? A 
glance at the diagram shows it to be the entire 
diameter of Mercury's orbit, or about 112 
millions of miles. 

Again, since Mercury shines by reflected 
light, it should exhibit phases. It does when 



The Planet Mercury. 121 

viewed through a telescope. Galileo in 1611 
discovered that Venus exhibited phases as soon 
as he turned the telescope to it. After what I 
have told you of the moon's phases, you will at 
once see that Mercury, a little after it has 
moved from the position M, will appear as a 
crescent; at M', M'", one half of it will be 
illuminated, and at M" it will be full. 

Since it is so much nearer to us at M, it 
should appear much larger, should it not? It 
does; its angular diameter as measured from 
the earth is 2 T / 2 times more at M than at M". 

When should we see it to most advantage, at 
M, M', or M"? If we take the distance, only, 
into consideration, we would say at M, where it 
appears so much larger. But it then only 
shows as a crescent, and is, besides, too near the 
sun to be seen to advantage. If we consider 
the light reflected by it, we would say at M", 
because it is full. But then it is farthest off, 
and appears at its smallest, besides being so 
near the sun again. 

It is brightest, in fact, at the positions M', 
M"', because, although only one half of it is 
illuminated, it is farthest from the sun (as we 
view it), and is less affected by its light. 

When Mercury is at its inferior conjunction it 
sometimes, though very rarely, passes across the 
face of the sun. This is called a transit of 



122 Familiar Talks on Astronomy, etc. 

Mercury. Astronomers cannot make use of it 
to determine the sun's parallax, as they do in 
the case of a transit of Venus. If the orbits of 
Venus and Mercury coincided with the plane of 
the ecliptic, there would be transits at every in- 
ferior conjunction. But they do not; just as 
we have seen that an eclipse of the sun does not 
happen at every new moon. 

What more do we know about Mercury? Its 
nearness to the sun prevents us from obtaining 
any very accurate knowledge of its surface ; but 
it consists of land and water, and is supposed to 
have an atmosphere ; and I may as well tell you 
here that all the planets are, so far as we know, 
similar to the earth. Lockyer says that a moun- 
tain in the southern hemisphere of Mercury is 
estimated to be 1 1 miles high. 1 



VENUS. 

We come now to Venus, the brightest of the 
planets, though far from being the largest. Its 
brightness is owing to its nearness. Its diameter 
is about 7,600 miles, and its mean distance from 
the sun is about 67,000,000 miles. It turns 
upon its axis once in 23 hrs. 16 min., 1 and it 
revolves about the sun in 224 days. 

1 See note, page 137. 



The Planet Venus. 123 

What I have just said concerning the different 
positions of Mercury in its orbit in relation to 
the earth, applies equally to Venus. 

In the diagram (Fig. 8) let S be the sun, E 
the earth, and V, V 7 , V", V", four positions of 
Venus in its orbit. Let E E' represent the orbit 
of the earth, and V V' V" the orbit of Venus. 

At V, Venus is in inferior conjunction; at V", 
in superior conjunction; and at V', V //r , in quad- 
rature, or its greatest eastern and western 
elongations. 

Venus never appears more than 47 degrees 
from the sun, and, of course, is never above the 
horizon at midnight. 1 The angle V E S, or the 
angle V"' E S, can never exceed 47 degrees. 
For some months of the year Venus is west of 
the sun, rises before it, and is known as the 
morning star ; 2 the remaining months it is east 
of the sun, sets after it, and is called the even- 
ing star, — "The star that bids the shepherd 
fold." When near the sun it is overpowered 

1 Yet Thompson, in the " Seasons " says : — 

" Sudden to heaven 
Thence weary vision turns ; where leading soft 
The silent hours of love, with purest ray 
Sweet Venus shines ; and from her genial rise, 
When daylight sickens, till it springs afresh, 
Unrivalled reigns, the fairest lamp of night " — 

which seems to mean that Venus rises at sunset and shines all 
night, which is impossible. 

2 Venus is an evening star for about 9 months ; for the next 
nine months she is a morning star. 



124 Familiar Talks on Astronomy, etc. 

by its light, and it is brightest at its points 
of elongation. 

Its distance from the earth varies greatly; 
it being nearest to us at inferior conjunction, 
and farthest at superior conjunction, — the differ- 
ence being the diameter of Venus' orbit; or 




Fig. 8. 

about one hundred and thirty- three millions of 
miles. It exhibits phases as Mercury does ; 
and, as in the case of that planet, the angular 
diameter of the crescent is much larger than the 
diameter when full ; it being then so much 
nearer. Indeed its angular diameter at inferior 
conjunction is about six and one-half times as 
great as when at superior conjunction. Venus 
can sometimes be seen in the daytime with the 



The Planet Venus. 125 

naked eye. It is then at one of its points of 
greatest elongation, and is at its brightest. The 
earth, as viewed at Venus, would appear about 
as Venus does to us, — a little brighter, because 
it is somewhat larger. 

Venus was called by the ancients Phosphorus 
or Lucifer, when the morning star; and Hes- 
perus or Vesper, when the evening star, — 
hence "Vespers." 

" How art thou fallen from heaven, O Lucifer, son 
of the morning ! " — Isaiah. 

" Hesperus, that led 
The starry host, rode brightest, till the moon, 
Rising in clouded majesty, at length 
Apparent queen unveiled her peerless light, 
And o^r the dark her silver mantle threw." 

— Milton. 

Astronomers tell us that Venus has an atmos- 
phere and water ; and Lockyer says that moun- 
tains are supposed to exist exceeding twenty 
miles in height ! 1 

One more point, and we will turn to another 
planet. 

When Venus is at V', in our diagram (Fig. 8), 
that is, at its greatest eastern elongation, the 
line E V being tangent to the circle V V V" at 
the point V, the angle E V' S is a right angle. 
Now in the right-angled triangle EV'Swe know 
1 See note, page 153. 



126 Familiar Talks on Astronomy \ etc. 

the angle S EV; and, although we may not 
know the actual value of S E (i. e. the distance 
of the sun from the earth), we can find the 
relative distances of the earth and Venus from 
the sun. For, taking the mean value of the 
angle S E V to be 46 , we have — 

, S V 

sine 46 = 



S E 



or, as the natural sine of 46 is .72 (the radius 
of the circle being assumed to be 1), 

.72 = |-^; hence S V, or S V = .72 S E. 

that is, the distance of Venus from the sun is 
about seven-tenths the distance of the earth from 
the sun. 

You recollect I told you in a former talk that 
astronomers knew these relative distances before 
they knew the sun's actual distance from the 
earth. You see now that as soon as we can 
assign a positive value to S E in miles, S V be- 
comes known also. We find S V by a transit 
of Venus, as I have described ; and I will again 
repeat that upon this distance depends the dis- 
tances of all the heavenly bodies, — save only 
the moon and the planet Mars. The moon's 
distance, and the distance of Mars you know 
we found by an independent method. 



The Planet Mars. 127 



MARS. 

The next planet is Mars. It is a superior 
planet; that is, its orbit is outside the earth's. 
Its diameter is about four thousand two hundred 
miles, and its mean distance from the sun is 
about one hundred and forty-one million miles. 
It turns upon its axis once in twenty-four hours, 
thirty-seven minutes ; and it makes one com- 
plete revolution about the sun in six hundred 
and eighty-seven days. So while its day is 
about the same as ours, its year is equal to 
nearly two of ours. 

In the diagram (Fig. 9) let S represent the 
sun, E the earth, and M, M', M", M'", the planet 
Mars, in four positions in its orbit. We will 
suppose the earth to be at E, at rest in its orbit 
EE'. 

When Mars is at M, it is said to be in opposi- 
tion (that is, opposed to the sun) ; and when at 
M", in conjunction (that is, conjoined with the 
sun). At M', M"', it is in quadrature. It is 
readily seen that when Mars is in opposition it 
is nearer the earth than at any other time. The 
difference in its distance at opposition and con- 
junction is the diameter of the earth's orbit; or 
about one hundred and eighty-five millions of 
miles ! 



128 Familiar Talks on Astronomy, etc. 

Again, we see that when it is in conjunction, 
it must rise and set with the sun ; whereas when 
it is in opposition, it must rise as the sun sets ; 
and it will be upon the meridian about midnight. 




M'" 



Fig. 9. 
This is, of course, the best time to observe it, 
and astronomers take advantage of it. It was 
in this position (opposition) when the observa- 
tions I have told you of were taken at Green- 
wich and the Cape of Good Hope to determine 
its parallax. Its angular diameter at opposition 
is seven times as great as in conjunction, as we 
might expect. 

Mars is the only one of the superior planets 
that exhibits a marked phase. It sometimes 
appears gibbous. 



The Planet Jupiter. 129 

Mr. Lockyer says : " Mars has not only land, 
water, and snow, like the earth, but also clouds 
and mists. The land is generally reddish when 
the planet's atmosphere is clear; this is due to 
the absorption of the atmosphere, as is the 
color of the setting sun with us. Hence the 
fiery red light by which Mars is distinguished in 
the heavens. The water appears of a greenish 
tinge." 

JUPITER. 

The next planet outside of Mars is Jupiter. It 
is not necessary to draw diagrams for it and the 
remaining planets, as Fig. 9 answers for all. 
The remarks as to Mars, in different positions in 
its orbit, applies to all the superior planets. 

Jupiter is the largest and, excepting Venus, 
the brightest of all the planets. Its diameter is 
about 86,000 miles, and its mean distance from 
the sun is about 480,000,000 miles. It turns 
upon its axis once in 9 hrs. 55 min., and makes 
one complete revolution about the sun in about 
12 of our years. 

We here are struck with the fact that while 
Mercury, Venus, the Earth, and Mars, rotate in 
about the same time (24 hours), Jupiter, though 
so very much larger, rotates in about 10 hours. 
Now, as the earth is supposed to have assumed 
its spheroidal shape in consequence of its rota- 
tion, we should expect to find Jupiter very much 
9 



130 Familiar Talks on Astronomy, etc. 

flattened at the poles. It is; the polar diame- 
ter being to its equatorial diameter as 16 to 17; 
while the earth's is only as 299 to 300. 

Mr. Lockyer says of Jupiter : " It is sur- 
rounded by an atmosphere so densely laden 
with clouds that of the actual surface we know 
nothing." 

SATURN. 

The next planet is Saturn. Its diameter is 
about 70,000 miles, and its mean distance from 
the sun is about 882,000,000 miles. It rotates 
in 10 hrs. 14 min., and revolves about the sun in 
about 29^ of our years. 

Saturn differs from the other planets in being 
surrounded by a series of rings. Astronomers 
are not yet agreed as to what these rings are 
composed of. The question belongs to what I 
have called speculative astronomy, and we will 
leave it to those who are spending years of their 
lives in trying to fathom it. 

URANUS. 

Our next planet is Uranus. It is about 
32,000 miles in diameter, and its mean distance 
from the sun is about 1 y^ billions of miles. It 
revolves about the sun in about 84 of our years. 
We do not know the time of its rotation because 
there are no spots on its surface to observe. 



The Planet Neptune. 131 



NEPTUNE. 

The last planet is Neptune, — so far off as to 
be invisible to the naked eye. Its diameter is 
about 35,000 miles, and its mean distance from 
the sun about 2^ billions of miles. It revolves 
about the sun in about 165 of our years. We 
do not know its time of rotation, nor do we 
know anything about its surface. 

Although I have given you the distances of 
the planets from the sun, I do not expect you 
to remember these exact figures. It is common 
in popular astronomies to give an idea of the 
distances of the heavenly bodies by calculations 
as to how long it would take to reach them, by 
cars, etc. I have much the same opinion of the 
value of such illustrations as the late John 
Phoenix, who says in his book: " It is a curious 
and interesting fact, much dwelt on in popular 
treatises on astronomy, that were a cannon-ball 
fired from the earth to Saturn, it would be 180 
years in getting there. The only useful de- 
duction that we are able to make from this fact, 
however, is that the inhabitants of Saturn — if 
warned of their danger by the sight of the flash, 
or the sound of the explosion — would have 
ample opportunity, in the course of the 180 
years, to dodge the shot." 



132 Familiar Talks on Astronomy, etc. 

I can, however, give you a rule by which you 
can always calculate the distance of the planets 
from the sun, supposing you to remember (as 
you should do) the distance of the earth from 
the sun. It is called Bode's law. 1 

If we write down, — 

o 3 6 12 24 48 96 

(which you observe is, from the second term, 
simply a geometrical progression), and add 4 to 
each, we get, — 

4 7 10 16 28 52 100 

and this series of numbers represents very 
nearly the relative distances of the ancient 
planets from the sun. For example, — 

4 7 10 16 28 52 100 

Mercury. Venus. The Earth. Mars. Jupiter. Saturn. 

Thus, we see that Mercury's distance from 
the sun is to the earth's as 4 to 10; Venus's as 7 
to 10; Saturn's as 100 to 10; and so on. It is 
very easy to remember this rule, and the dis- 
tances are correct enough for the ordinary 
student. For example, the mean distance of 
Venus from the sun is about 67,000,000 miles ; 
by Bode's law it is 65,000,000 miles. 

You notice I left a blank under the number 
28 ; this I will explain farther on. 

I have said that most of the planets have 

1 Kepler was the first to discover Bode's Law. (Chambers's 
End.) 



Jupiter s Satellites. 133 

satellites, or moons. They all have but Mercury 
and Venus. So far as we know, they are similar 
to our moon, and have the same motions, — ex- 
cept that the satellites of Uranus and Neptune 
seem to have a retrograde motion ; that is, they 
move from east to west, instead of from west to 
east, as the planets do. 

Jupiter has four moons. You can see them 
with an ordinary opera-glass, if you will select a 
time when Jupiter comes on the meridian about 
midnight; that is, when Jupiter is nearest the 
earth and is better defined. The dimensions of 
these satellites have been calculated, and names 
assigned them. They are all (but one) some- 
what larger than our moon. 

They revolve about Jupiter, and, as a matter 
of course, sometimes pass across his disk (a 
transit) ; sometimes pass behind him (an oc- 
cupation) ; and sometimes pass through his 
shadow (an eclipse). The occultations and 
eclipses occur very frequently, as you can 
imagine with four moons revolving about him. 

Astronomers can calculate and predict the 
times of these eclipses and occultations for 
years ahead, to the very second ; and use is made 
of them to determine the longitude, — that is, 
on shore ; we cannot observe them at sea, as I 
will explain to you in another talk. But you 
see that what I said is true as to theoretical 
astronomy being an exact science. 



TALK THE NINTH. 

Recapitulation. Discovery of the Velocity of Light. 
The Asteroids. Are the Planets Inhabited? Change 
of Seasons at Jupiter and Mercury. Aberration of 
Light. Kepler's Laws. Determination of the Density 
and Mass of the Earth. Density of the Planets. The 
Planets' Motions in their Orbits. 

OEFORE commencing this talk, let us look 
back on the last. We now know the names 
of the planets, their motions, distances from the 
sun, diameters, and volumes ; the length of their 
years and days, and something about their 
physical constitution. We concluded our last 
talk with an allusion to the occultations of 
Jupiter's satellites. 

We have seen that the telescope was first 
used by Galileo about the year 1610, and that 
he discovered the satellites of Jupiter. In 1675 
Roemer, a Danish astronomer, discovered the 
velocity of light. 1 He found that light was not 
transmitted instantaneously, as had been previ- 
ously supposed, but that it travelled at the rate 
of about 185,000 miles a second. Very rapid 
travelling, is it not? But if you will divide the 

1 See note at end of talk. 



The Velocity of Light. 135 

sun's distance from the earth by 185,000, you 
will find that light is about 500 seconds (or 8 
minutes and 20 seconds) in reaching us from 
the sun ; and of course much longer in reaching 
us from the stars, — hundreds, and even thou- 
sands, of years, astronomers say. Can you 
imagine it? 

You know that sound travels about 1150 feet 
in a second; very slowly in comparison to light. 
The speed of a tortoise compared to a " streak 
of lightning." 

Surveyors have made use of the velocity of 
sound to determine the length of a base-line. 
A gun is fired at one end of the line, and the 
observer at the other end watches the flash, and 
notes the number of seconds by his watch 
before he hears the sound. This multiplied by 
1 150 gives the length of the line in feet. To 
eliminate the effect of the wind, a gun is fired at 
each end of the line, and the mean time is 
taken. Of course, in this case the transmission 
of light is supposed to be instantaneous, which 
it is for so short a distance. This method of 
measuring a base-line is not much used now; it 
is not accurate enough. 

But how did Roemer discover the velocity of 
light? By the occultations of Jupiter's satel- 
lites. The times of these occultations are pre- 
dicted (as I have told you) and inserted in the 
astronomical almanacs. 



136 Familiar Talks on Astronomy, etc. 

Now, Roemer observed that these occultations 
happened 16 min. 26 sec. later when Jupiter 
was in conjunction than when it was in opposi- 
tion. (See Fig. 8). Jupiter, you see, is about 
185 millions of miles farther off when in con- 
junction than when in opposition. 

What idea naturally occurred to Roemer? 
Why, that light did not travel instantaneously; 
but that it took 16 min. 26 sec. to traverse the 
diameter of the earth's orbit. This distance is 
about 185,000,000 miles; divide it by 16 min. 
26 sec, or 986 seconds, and you have the 
velocity of light per second. Very simple, is it 
not? And I again call your attention to the 
manner in which astronomers go on building up 
the science, step by step, like the " House that 
Jack built" Jansen invents the telescope ; with 
it Galileo discovers the satellites of Jupiter; and 
by the occultations of these satellites, Roemer 
discovers the velocity of light. 

The velocity of light can be, and has been 
calculated by other methods, which it is not 
necessary in these talks to explain. 

I have said that the planets belonging to our 
system were Mercury, Venus, the Earth, Mars, 
Jupiter, Saturn, Uranus, and Neptune. Now, I 
am quite prepared to hear you say you have fre- 
quently seen in the papers that " a new planet had 
been discovered." This I must tell you about. 



The Asteroids. 137 

The distance between Mars and Jupiter is 
very great. If you will look back to the series, 
given under Bode's Law, page 132, you will see 
I left a blank under the number 28. Astrono- 
mers finding that this Law gave the distances of 
the planets from the sun pretty nearly, provided 
they skipped 28 and placed Jupiter under 52, 
jumped to the conclusion that there must be a 
planet somewhere to fill the unoccupied place. 
Search being made, a very small planet was dis- 
covered in 1800 and named Ceres; and soon 
after, three others, — Juno, Pallas, and Vesta. 
The search has been continued with constantly 
improving telescopes, until now we know of 
about 265 of these very small bodies. They 
have all received names ; but of course we can- 
not pretend to remember them. 

These bodies are known as the asteroids, or 
minor planets. The theory in relation to them 
is, that " once upon a time " a large planet ex- 
isted in this space, and that it burst into innu- 
merable fragments ; perhaps by coming into 
contact with some other celestial body. 1 

1 Professor A. Hall of the U. S. Navy, the discoverer of the 
satellites of Mars, who has kindly looked over my MSS., writes 
me that astronomers doubt this theory. He also tells me that 
the times of rotation of Mercury and Venus are not well known, 
and that it is doubtful if any mountains on Mercury and Venus 
have been measured. 

He suggests to me that Jupiter's satellites may have been 
seen by the Ancients from the tops of high mountains. 



138 Familiar Talks on Astronomy, etc. 

These asteroids are very small bodies, and 
they are invisible to the naked eye ; indeed, it 
requires very careful observation with a power- 
ful telescope to see them at all. The largest of 
them is but 228 miles in diameter. The force 
of gravity there must be very small. A man on 
one of them would spring with ease 60 feet high, 
and come down without a shock to his system. 
Indeed, on the least of them, a man would have 
to be careful not to practise gymnastic exercises 
at all. If, for instance, he should attempt the 
" high jump," he would perhaps ascend so high 
as to be beyond the attraction of gravitation of 
the asteroid. He would then be attracted by 
some other heavenly body, and would pass the 
remainder of his melancholy existence in whirl- 
ing through space. To use Macbeth's words, — 

" He 'd jump the life to come." 

I have said that the planets are similar to our 
earth. One question presents itself: are they 
inhabited? 

It is reasonable to suppose they are. Why 
should the earth, which is only one of the 
planets, alone be inhabited? But if they are, 
the inhabitants must be differently constituted 
physically from ourselves, as you must perceive. 

Mercury, for instance, is thirty-six millions of 
miles from the sun, — a little more than one- 
third of our distance. It receives from the sun, 



Jupiter's Seasons. 139 

at times, ten times as much heat as the earth, 
never less than seven times as much. We could 
not live under such a temperature. 

Neptune, nearly three billions of miles from 
the sun, receives only one-thousandth as much 
heat as we do. The climate of the Frigid Zone 
is nothing in comparison to its cold. We cer- 
tainly could not support it. 

Moreover, while the force of gravity on the 
surface of Mercury is but three-fifths of that at 
the earth's surface, the force of gravity on the 
surface of Jupiter is very much greater. We 
might stand the former, — it would make us 
more springy in our walk, — but not the latter. 
It is calculated that the force of gravity on the 
sun's surface is twenty-seven times as great as 
at the earth; and that if one of our inhabi- 
tants were carried there, he " would be literally 
crushed by his own weight." 

Do you remember that in our talk about the 
Change of Seasons I made a supposition in ref- 
erence to the inclination of the axis of the earth? 
I supposed the axis of the earth to be perpen- 
dicular to the plane of the ecliptic, and called 
your attention to the fact that there would be 
no change of seasons. Well, the axis of Jupiter 
has little or no inclination, and there is no 
change of seasons there. At Mercury, on the 
contrary, — his axis being greatly inclined, — 



140 Familiar Talks on Astronomy, etc. 

the change of seasons is violent, as I explained 
to you it would be if the angle between our 
equator and ecliptic were very much increased. 

I have not yet told you anything about what 
is called the Aberration of Light. This is caused 
by the motion of the earth and the velocity of 
light. You know that in a rain-storm, should 
the air be absolutely at rest, the rain-drops fall 
perpendicularly, and a man exposed to them 
would receive them on the crown of his hat as 
long as he stood still; should he start to run, 
the drops appear to fall in a slanting direction, 
and will strike him in the face. It is just so 
with a ray of light, the earth being in motion. 
The effect is that a star seems to describe a 
small circle in the heavens. 

The telescope, in observing a star, has to be 
pointed slightly in advance of the star, and there 
is an apparent displacement. When the motion 
of the earth is directly towards a star there is 
no aberration. It is greatest when the earth's 
motion is at right angles to the direction of the 
star. This you must clearly see, for it would be 
the same with our man in the rain. 

I will not attempt to go farther into this sub- 
ject ; but will mention that the velocity of light 
has been determined by its aberration, and 
that the fact of there being an aberration is one 
of the proofs that the earth revolves about the 



Kepler s Laws. 141 

sun. The " correction " for aberration is a very 
small quantity ; we have diurnal aberration, and 
annual aberration ; corresponding to the daily 
and yearly motions of the earth. 

Aberration was first explained by Bradley, 
the astronomer royal, somewhere about 1750. 
He was led to its discovery by observing the 
pennant of his boat while rowing on the 
Thames. 

About the year 1610 an astronomer named 
Kepler announced three remarkable laws. They 
have been called empirical laws, — from the fact 
that although Kepler believed them to be true, 
he could not explain why they were true. This 
was reserved for Sir Isaac Newton, who some 
fifty years after, discovered the law of universal 
gravitation, which law explained Kepler's laws. 

You should commit to memory these laws. 
They are as follows : — 

1. Each planet describes round the sun an elliptical 
orbit, and the centre of the sun occupies one of the 
foci. 

2. The radius-vector of a planet describes equal ' 
areas in equal times. 

3. The squares of the periodic times of any two 
planets are proportional to the cubes of their mean 
distances from the sun. 

The radius-vector is a line supposed to be 
drawn from the sun to the planet; and the 



142 Familiar Talks on Astronomy, etc. 

" periodic time " of a planet is the same thing 
as its year, or time of revolution about the sun. 
You observe that by the third law, we can 
very readily calculate the distance of a planet 
from the sun, when we know its periodic time, 
which is very easily found by observation. 
For example, suppose we know the periodic 
time of Venus to be two hundred and twenty- 
four days, and we wish to use the third law to 
compute its distance from the sun, — using the 
earth, we have — 

365 X 2 ' 224 2 : : 93,000,000 s : x z . 

Having found x 3 we extract its cube root, and 
the result is the distance required. 

So also if we discover a new planet, we 
have only to observe it until we have found 
its periodic time, and then apply this third law, 
which enables us to compute its approximate 
distance, at least, in a few minutes. 

Before concluding this talk, I have one more 
point to call to your attention. Perhaps you 
have already noticed its omission. I have given 
you the diameters, and volumes of the sun and 
planets; but I have not said anything about 
their masses. Your books tell you that mass is 
a different thing from volume. The volume of 
a body has reference to the cubical contents of 
the body, or its size. The mass of a body is 



The Ear tit s Density. 143 

the quantity of matter it contains. 1 When we 
know the volume and mass of a body, we can 
find its density, or specific gravity. 

You remember that when we attempted to 
find the distances and diameters of the sun, 
moon, and planets, our first step was to find 
the exact dimensions of the earth. Well, be- 
fore we can calculate the masses of the sun, 
moon, and planets, we must first find the mass 
of the earth. 

This calculation depends upon Newton's " Law 
of Universal Gravitation." It is entirely too ab- 
struse to introduce into these talks. To read 
Newton's " Principia," or Laplace's " Mecanique 
Celeste," understanding^, requires great knowl- 
edge of mathematics. I am only going to try 
to give you an idea of how Newton's law is 
applied to the determination of the mass and 
density of the earth. 

Newton's law may be thus stated : the force 
with which two material particles respectively 
attract each other is directly proportional to 
their masses, and inversely proportional to the 
square of the distance between their centres. 

The density of the earth, or its specific gravity, 
has been determined in three ways : — 

1 Mass must not be confounded with weight. The weight 
of a body is the apparent force with which it is attracted to- 
ward the centre of the earth, and this varies. The weight of 
a body is greater at the poles than at the equator and is less 
at high altitudes than at the surface of the earth. 



144 Familiar Talks on Astronomy, etc. 

i. By comparing the attractive force of a large 
metallic ball of known size and density, with that of 
the earth. 

2. By finding how much a large mountain will de- 
flect a plumb-line, or draw it towards itself from the 
perpendicular. 

3. By determining the rate of vibration of the same 
pendulum on the top and at the bottom of a moun- 
tain, or at the bottom of a mine, and at the Earth's 
surface. 

The first method is known as the Cavendish 
Experiment. In Airy's lectures you will find 
a full explanation of it. It is too difficult to 
explain here. 

In 1772, the English astronomer and mathe- 
matician, Maskelyne, proposed to the Royal 
Society to try the second method. Accord- 
ingly, he went in 1774 to a very high mountain 
called Schehallien, in Perthshire, and there he 
measured the inclination or deflection of the 
plumb-line on each side of the mountain. Ac- 
cording to the theory of gravitation, — suppos- 
ing the earth to be an exact sphere, — the lead 
at the end of the line should point directly to- 
ward the centre C of the earth (Fig. 10) if the 
mountain did not disturb it; and if the plumb- 
line is taken to two places a certain distance 
apart and its inclination measured by means of 
celestial observations, it is easy to find out how 
much the lines D F, D' F', will incline toward 



The Earttis Density. 



145 



each other when no mountain is between them. 
This being known, Maskelyne then made two 
observations, one on each side of Schehallien, 
and found that in this case the inclination, in- 
stead of being from D to F, and from D' to F', 
on each side, was from E to F, and from E' to 
F', because the mountain attracted the lead to- 



E D 



tf E 




ward itself on either side. So the deflection 
E F D, or E' F' D', through which the plumb- 
line was drawn from the perpendicular showed 
the difference between the attraction of the 
whole earth and the attraction of the mountain. 
See Fig. 10; A B is the surface of the earth; 
D C D' the angle formed by two plumb-lines 
10 



146 Familiar Talks on Astronomy, etc. 

pointing to the centre of the earth ; and EGE' 
the angle formed by the two plumb-lines, when 
drawn aside by the mountain, M. 

Dr. Hutton, the celebrated mathematician, 
calculated the size and weight of Schehallien. 1 
This he did by surveying it and measuring it 
in every direction, and then taking pieces of the 
different rocks it contained and weighing them 
carefully. When this was done it was found 
that the mountain pulled half as strongly in 
comparison to its size as the earth did for its 
size. This showed that the materials in the 
mountain were half as heavy as the average of 
those in the earth generally ; and as they were 
also about 2]/ 2 times as heavy, bulk for bulk, as 
water, it was proved that the whole globe is 
about five times heavier than it would be if it 
was made entirely of that fluid. 

The above illustration is from Buckley's " His- 
tory of Natural Science." You will find a full 
explanation of this experiment in " Airy's Lec- 
tures," and you will also see how intricate the 
calculations are. It is sufficient for us to know 
that the density of the earth as compared to 
water is as 5.45 to 1. And I will tell you here 
that the planets increase in density as they ap- 
proach the sun; Mercury being the densest, 

1 The Encyclopaedia Britannica says : " Playfair estimated 
with greater accuracy the mass of Schehallien, and obtained 
4.7 for the earth's mean density. 



The Densities of the Planets. 147 

Venus, the Earth, and Mars about of the same 
density, Jupiter only one-fifth as dense as the 
Earth, and Saturn, Uranus, and Neptune still 
less dense than Jupiter. The density of the sun 
is one fourth the earth's density. 

The earth's density being found, its mass is 
easily calculated ; and knowing the earth's mass, 
the masses of the sun, moon, and planets have 
been computed. 

Thus we see that a planet revolves about the 
sun because of the attraction of gravitation. 
Referring to this Law of Gravitation, the poet 
Rogers says, — 

" That very law which moulds a tear 
And bids it trickle from its source, 
That law preserves the earth a sphere, 
And guides the planets in their course." 



ON THE VELOCITY OF LIGHT. 

Mr. Richard Proctor the astronomer says : — 
" If light did not travel with a velocity enormously exceed- 
ing that of the planets in their orbits, they would seem to 
move very irregularly, — at least until the cause of the irregu- 
larity had been discovered; we should sometimes see Mars, 
for example, where he was a month or so before, sometimes 
where he was a year or so before, — i. e., sometimes twenty or 
thirty millions of miles, sometimes two or three hundreds of 
millions of miles, from his true place. As it is, light crosses 
the greatest distance separating us from Mars in about twenty 
minutes, and the least in about four minutes, so that the ir- 
regularity in his apparent motions never amounts to more 



148 Familiar Talks on Astronomy, etc. 

than the distance he traverses in about sixteen minutes, or a 
little more than fourteen thousand miles. If light travelled 
at the same rate as sound, it would have been absolutely 
impossible for men to interpret the apparent planetary mo- 
tions, and the most erroneous ideas would inevitably have 
prevailed respecting the real motions. Even if the velocity 
of light had amounted to twenty or thirty miles per second, 
instead of its real value — about 186,000 miles per second — 
the true theory of the planetary movements would have 
seemed absolutely inconsistent with what the eye would have 
seen. Even as it is, astronomy is directly opposed to the doc- 
trine that 'seeing is believing/ We see every celestial body* 
not where it is, but where it was. It is hardly necessary to 
remark that astronomy, in predicting the motions of the celes- 
tial bodies, as well as the occurrence of eclipses, transits, 
occultations, and so on, takes this circumstance fully into 
account." 



TALK THE TENTH. 

The Stars, — their Number; Magnitude; Parallax; Dis- 
tance. Colored Stars. The Constellations. Geog- 
raphy of the Heavens. Use of Globes. The Zodiacal 
Constellations. Classification of the Stars. The Milky 
Way. Double Stars. Variable Stars. Star-Clusters. 
Nebulae. The Magellanic Clouds. Meteors. Meteor- 
ites. Star-Showers. Comets. Star-Dials. Preces- 
sion. Nutation. 

WE have so far talked of the earth, the 
moon, the sun, the planets, and their 
satellites ; that is, we have confined ourselves to 
our solar system. Let us now turn our atten- 
tion to the stars. 

You remember I told you in our first talk that 
the early observers soon noticed a difference 
between the planets and the stars. They found 
that while the latter were " fixed," the former 
changed their positions among them. Another 
thing they probably noticed, — the planets shine 
with a steady light; the stars "twinkle." 

" And nimbly tumbling out of bed, 
The little stars commence to twinkle." 

Campbell, speaking of the approach of night, 
says, — 

" And sentinel stars set their watch in the sky," — 



150 Familiar Talks on Astronomy, etc. 

which very prettily describes the appearance as 
the stars of the first magnitude first become 
visible at the approach of night. 

The planets shine by reflected light; the stars 
shine by their own light. Every star is, in fact, 
a sun, and like the sun an incandescent mass ; 
and each one is probably the centre of a system, 
and surrounded by planets just as our sun is. 
The sun is a star ; and although to us so large 
and bright, its size is small compared to some 
of the stars. Why, it is conjectured by astron- 
omers that if the sun were removed to the mean 
distance of the first-magnitude stars, it would 
appear as a star of the sixth magnitude. 1 

The number of stars seems to be unlimited. 
With the naked eye it is supposed that 6,000 
can be seen; that is, 3,000 at any one time. 
This embraces stars up to the sixth magnitude; 
but it depends upon a person's eyesight, of 
course. But with the telescope millions are re- 
vealed ; and as telescopes are constructed with 
greater magnifying power, more and more stars 
are seen. No wonder that Milton says, — 

'• Innumerable as the stars of night." , 

With powerful telescopes 20,000,000 are visi- 
ble, but of course only a fraction of this number 

1 This admits of a doubt, however. 



Magnitude of the Stars. 1 5 1 

have been catalogued ; that is, their right ascen- 
sions and declinations calculated. 

Still, the German astronomer Argelander has 
issued a catalogue containing the positions of 
324,000 stars. Think what work is involved in 
this! 

There are 20 stars of the first magnitude, 
65 of the second, 300 of the third, 450 of the 
fourth, and so on up to the fourteenth, increas- 
ing largely in number as we descend in the 
scale of brilliancy. You can commit to mem- 
ory the names of the bright stars in a few 
minutes; they are, in the order of their bright- 
ness, Sirius, Canopus, Alpha Centauri, Arcturus, 
Rigel, Capella, Vega, Procyon, Betelgeuse, Ach- 
ernar, Aldebaran, Beta Centauri, Alpha Crucis, 
Antares, Altair, Spica, Formalhaut, Beta Crucis, 
Pollux, and Regulus. 

But what do we mean by magnitude? Not 
size, — we know nothing about the size of the 
stars, — we mean brilliancy. The brightest are 
called stars of the first magnitude ; the next, 
stars of the second magnitude, and so on to the 
fourteenth magnitude. Of course this rule is 
approximate, for all stars of the same magni- 
tude are not precisely of the same brilliancy. 
Sirius, the brightest of all the stars, is nearly 
three times as bright as the other first-magni- 
tude stars. In the star-catalogues you will see 
marked against a star, " I. 2." This means that 



152 Familiar Talks on Astronomy, etc. 

it is between the first and second magnitude, 
and so on. 

The stars appear as mere points of light, even 
with the most powerful telescopes. We cannot, 
therefore, determine their angular diameters. 
The best instruments in the world cannot 
measure the angle subtended by a star's disk. 
What follows from this? Why, they must be 
immensely far off. The sun subtends an ap- 
preciable angle (about 33') ; yet the stars, 
although much larger — as we suppose — 
subtend none. 

Can we determine their distance? Let us see 
how astronomers have tried to do so. You 
remember the moon's distance was found by 
measuring its zenith distance, — the two ob- 
servers being far apart on the surface of the 
earth, — and thus finding its parallax. Having 
found its parallax, its distance was easily com- 
puted. The distance between the observers was 
the base-line of the operation. 

Now, when we use this method with the stars, 
we can get no result. The parallax cannot be 
discovered. I will repeat that the parallax we 
are trying to find is the angle subtended at the 
star by the distance between the two observers ; 
or it is the difference in the apparent direction 
of the star, as seen by the two observers. But 
it matters not how far apart the observers may 
be placed, — even if one were at the north pole, 



Distance of the Stars. 153 

and the other at the south pole, — the stars are 
always seen in the same direction; that is, no 
parallax is discovered. 

This method will not do, then. It answers 
for the moon, which is only 240,000 miles off, 
but it will not do for the stars. Indeed, we 
have seen that it will not do for the sun; and 
the sun is much nearer to us than the nearest 
star, though it is 93,000,000 miles off. The 
base-line is evidently too small. Can we find a 
longer one ? Yes ; as the earth moves half-way 
in its orbit in six months, we may use the diam- 
eter of the orbit itself as a base; that is, a 
base-line 185 millions of miles long. We have 
certainly increased our base-line very much. 
What is the result? Surely, now, we must find 
some parallax ! No ; wonderful to say, although 
we have moved 185 millions of miles, the stars 
appear still in the same direction. Does not 
this convey to the mind the idea of immense 
distance? 

Light travels, as we have seen, about 185,000 
miles a second ; and it is conjectured by astron- 
omers that if a star of the sixth magnitude were 
destroyed, we should continue to see it in the 
heavens for 120 years; and if one of the twelfth 
magnitude were now created, it would be 3,500 
years before its light would reach the earth. 

Bessel, the great German astronomer, by a 
method which I need not explain here, did, 



154 Familiar Talks on Astronomy, etc. 

however, discover the parallax of the small star, 
61 Cygni ; and by his method the parallax and 
distance of nine stars have been found. The 
nearest star is Alpha Centauri; and when I tell 
you its parallax is but seven tenths of a second 
(of arc) you will comprehend the extreme 
difficulty of the problem. From the parallax of 
Alpha Centauri its distance has been computed. 
It is found to be 224,000 times the distance of 
the sun, — that is, 93,000,000 multiplied by 
224,000 ; these figures are so great that the 
mind fails to grasp them. 

As the stars are of different degrees of bright- 
ness, so are they of different colors. Most of 
them appear white, but a few shine with another 
light. Thus, Aldebaran and Antares are red; 
Capella, Spica, and a few others blue; Sirius, 
Altair, and two others green ; x and Arcturus, 
yellow. With the exception of the red stars, 
however, they appear generally white ; and, so 
far as the color is concerned, they all look alike. 
How, then, do we distinguish them? 

If I were walking with one of you on a 
cloudy night, and a single star should peep out 
between the clouds, and you should ask me 
what star it was, I would answer that I did not 
know. I might say it looked like a star of the 

1 Professor Lockyer says this ; but I have never noticed a 
greenish hue myself, and to me Spica appears red. 



The Constellations. 155 

first magnitude ; or, if very bright, that it might 
be Sirius ; or, if red, that it might be Aldebaran, 
or Antares ; but I could not say positively what 
star it was. How could I when they all, or 
nearly all, look alike? I should be inclined to 
quote Sancho Panza, and say : " In the night all 
cats are gray." 

Now, you know a sailor determines his posi- 
tion at sea by what he calls his " bearings." 
Well, it is just so that we find a particular star 
in the heavens ; we see how it bears from cer- 
tain other stars. (I am speaking of an observer 
viewing the heavens with the naked eye. As- 
tronomers, in their observatories, can find any 
star by its right ascension and declination ; and 
indeed, as they generally use stars of the fifth or 
sixth magnitude in their observations, some of 
them do not know the bright stars when they 
see them. They do not pay much attention to 
what we call the geography of the heavens). 

It is for this reason astronomers have grouped 
the stars under the name of " constellations." 
I do not refer to the figures of lions, bears, 
dragons, etc., found on celestial maps. No 
mortal man could ever trace them out, and 
astronomers pay no attention to them. But 
there are some which present figures plain 
enough to distinguish, and by these constella- 
tions we find the stars. There are one hundred 
and nine of these groups. Some of them re- 



156 Familiar Talks on Astronomy, etc. 

ceived their names fifteen hundred years before 
the Christian era; and all the principal ones 
were known before Christ. Some of the bright- 
est stars are still called by the Arabian or other 
names by which they were formerly known: 
Thus, Alpha Canis Majoris is called Sirius; 
Alpha B otitis, Arcturus ; Alpha Tauri, Alde- 
baran; Alpha Ursce Minoris, Polaris, or the 
pole star, etc. 

The constellation which you should all be 
able to point out is Ursa Major, the great 
bear; because by the arrangement of seven 
stars in it we can find the pole or north star. 
These seven stars form a " dipper," and two 
stars in it, called the " pointers," always point to 
the pole star, which star is in Ursa Minor, the 
little bear. If you do not know the pole star, 
get some one to show you how to find it by the 
" pointers," without loss of time. Every one 
should know how to find the pole star, at least. 
Again, the three bright stars in the belt of 
Orion point to Sirius; Aldebaran is in the leg 
of a V-shaped constellation, etc. ; and, as I said 
in our first talk, as the stars are " fixed," these 
figures or constellations are unchangeable in 
form. The " dipper," in our latitude (say 
40 N.) revolves about the pole star, and is 
always above the horizon. Although we see 
it, sometimes to the right of the pole star, and 
at others to the left, — sometimes above it, and 



On the Use of the Globes. 157 

again below it, — at times right side up, and 
at others inverted ; yet it always preserves the 
figure of a " dipper," and the " pointers " point 
steadily to the pole star. 

It is a very interesting study to observe the 
heavens at night, and to be able to point out 
the stars and constellations, and give their 
names ; but you must not imagine this to be 
Astronomy ; as I fear it is too often supposed 
to be. If, in your study of geography, your 
teacher had required you to simply learn the 
names of the cities and countries of the world 
and say: Berlin is in Prussia, Lima is in Peru, 
Chimborazo is in Ecuador, etc., you would not 
know much geography, would you? You would 
wish to know something about the structure of 
the earth, the manners and customs of the in- 
habitants, and many other things. Well, so it 
is with the geography of the heavens and as- 
tronomy. It is all very well to know the names 
of the stars and how to find them; but as- 
tronomy tells us of the motions, distances, di- 
mensions, physical constitution, etc., of the 
heavenly bodies. 

I do not know whether the " globes," and 
their use, is generally taught in our schools. 
In England their use in young ladies' seminaries 
is, I believe, universal. I think it was Thackeray 
who said he doubted if any young lady ever 



158 Familiar Talks on Astronomy, etc. 

really did learn the " use of the globes." I will 
not be as cynical as that, because I have not 
much used the " globes " myself, and am not 
qualified to say to what extent they assist the 
student to comprehend astronomical problems. 
All minds differ. Some of you in your mathe- 
matical course liked algebra, others preferred 
geometry ; some like to get at the truth by ab- 
stract reasoning, others want a graphic illustra- 
tion. In the study of astronomy, then, if you 
find you can better think it out, do so (it is by 
far the best way) ; if you find you can do better 
with a diagram, draw it; and if you find that 
an orrery, or a globe, or a celestial map, assists 
you, use it. 

Perhaps you all know the zodiacal constella- 
tions, as they are called. You see frequent 
mention of them in your books. What are 
they called for? The zodiac. 

The zodiac is a portion of the heavens, ex- 
tending nine degrees on either side of the 
ecliptic, in which the sun and major planets 
appear to perform their annual revolutions. 
The twelve constellations through which the 
sun passes in his annual round, are called the 
zodiacal constellations. Their names are : Aries, 
Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scor- 
pio, Sagittarius, Capricornus, Aquarius, and 
Pisces. 



The Zodiacal Constellations. 159 

The zodiacal constellations must not be con- 
founded with the Signs of the Zodiac. The point 
where the sun crosses the equator at the vernal 
equinox (March 21), that is, at the intersection 
of the ecliptic and the equator, was, in the time 
of Hipparchus, — 2,000 years ago, — in the con- 
stellation Aries, and it was called the first point 
of Aries. 

At that time the sun was in Aries at the 
vernal, and in Libra at the antumnal equinox. 
Owing to what is called the precession of the 
equinoxes (which I will tell you about presently), 
the sun is now in Pisces at the vernal, and in 
Virgo at the autumnal equinox; and it is con- 
stantly changing, though very, very slowly. 

What stars are mentioned in the Old Testa- 
ment? The Pleiades, Arcturus, and Orion. 

Canst thou bind the sweet influences of Pleiades, 
or loose the bands of Orion ? — yob. 

Which maketh Arcturus, Orion, and Pleiades. — yob. 

Having seen how astronomers group the stars 
into constellations, let us now inquire into the 
manner of classifying and naming them. The 
method now in use, introduced by Bayer of 
Augsburg, in 1603, is to arrange all the stars in 
each constellation in the order of brightness, 
and to attach to them, in that order, the letters 
of the Greek alphabet, using, after the letters, 



i6o Familiar Talks on Astronomy, etc. 

the genitive of the Latin name of the constella- 
tion. Thus : Alpha Lyrce denotes the brightest 
star in the Lyre ; Beta Centauri, the next to the 
brightest in the Centaur, and so on. After the 
Greek alphabet is exhausted, the Roman alpha- 
bet is used in the same way; and after that, 
recourse is had to numbers. Thus: 61 Cygni 
is a very small star in the Swan. 

The milky way, — Via Lactea, — sometimes 
called the galaxy, — which you cannot fail to 
have observed, is composed of stars so faint and 
apparently so near together that the eye can 
perceive only a dim, continuous glimmer. This 
causes the whitish appearance. Thus Sir John 
Suckling says, — 

" Her face is like the milky way i' the sky, 
A meeting of gentle lights without a name." 

With powerful telescopes astronomers discern 
double-stars, variable stars, star-clusters, and 
nebula. The term nebula was formerly applied 
to everything in the sky which appeared cloud- 
like to the naked eye or in a telescope. Now, 
a nebula is supposed to be a mass of incan- 
descent gas. It is foreign to my purpose to 
say anything here concerning what is called the 
nebular hypothesis , save only that it is a specula- 
tion as to how the stars, planets, and satellites 
were first formed. 



Meteors and Comets. 161 

When Magellan got pretty far south on his 
voyage around the world in 15 19, he observed 
two cloudy oval masses of light, which have 
since been called the Magellanic Clouds. They 
look very much like cirrus clouds, — but Magel- 
lan must have soon noticed that they were not 
clouds, from the fact that they did not move 
with the wind, but preserved their relative po- 
sitions to the stars; moreover, they appeared 
night after night. These clouds are said by 
astronomers to be star-clusters, and nebulous 
matter in various degrees of condensation. 

Now let me say something about two other 
heavenly bodies, not yet mentioned by me, — 
meteors and comets. 

We frequently see at night what we call 
shooting stars. They are what astronomers call 
meteors. These small bodies are opaque, and 
travel around the sun. Sometimes the earth in 
its orbit passes through them, and we have a 
star-shower. These showers may be expected 
to occur in the months of August and Novem- 
ber. The most famous one of which we have 
any account occurred in this country in Novem- 
ber, 1833. 

But if these bodies are opaque, how is it that 

they emit such a bright light? It is owing to 

the fact that they enter our atmosphere at the 

velocity of about thirty miles a second, and the 

11 



1 62 Familiar Talks on Astronomy, etc. 

friction sets them on fire. Most of them are en- 
tirely consumed; but occasionally one is found 
large enough to resist the action of the atmos- 
phere, and falls to the earth. This is called a 
meteorite. They are divided into three classes 
to indicate their structure ; they are stone, iron, 
or intervening varieties. 

When we go back to the records we find that 
a large number of meteorites are known to have 
fallen. Some have killed men and cattle, and 
buildings have been set on fire by them. They 
have been known to fall in showers ; and, indeed, 
I read of such a shower happening in the Argen- 
tine Republic only a few years ago. In a case 
of the kind one would be likely to " come in 
out of the rain," without waiting to be told. 
You will find specimens of meteorites in most 
museums. 

We occasionally see in the heavens masses — 
probably white-hot — called comets, which shine 
by their own light. They circle around the sun 
in a variety of orbits ; some of them are ellipses, 
some parabolas, and some hyperbolas. Some 
move from west to east (as the planets do), and 
others from east to west. The comets having 
elliptical orbits return again to our system, 
and their periods have been calculated; those 
whose orbits are parabolic or hyperbolic never 
return. 



Comets. 163 

Of what are these eccentric bodies com- 
posed? There is first, the head, or coma; in 
the head (sometimes) a bright spot like a 
star, called the nucleus ; and lastly, the tail. 
The nucleus is the brightest, then the coma, 
and then the tail. The tail is sometimes mil- 
lions of miles long. 

What do we know of their physical consti- 
tution ? In the case of a comet without a 
?iucleuSy the coma is probably a mass of white- 
hot gas. The tail is even lighter, and may 
be regarded as the waste, so to speak, of the 
coma. Stars can be seen through both the coma 
and the tail. What the nucleus is, we do not 
know. x 

Comets are very eccentric in their move- 
ments. Sometimes they move towards the 
sun, at others away from it; and sometimes 
they appear to be coming head-first for the 
earth. In former days this gave rise to great 
apprehensions. 

You may recollect that Stephenson was the 
inventor of locomotives and railroads. Some- 
one objected that a locomotive might come 
into collision with a cow. " So much the worse 
for the coo," replied Stephenson, in his broad 

1 Professor Keeler, of the Lick Observatory, says that 
carbon seems to be a constituent of most comets, and that 
some comets probably have dense nuclei of considerable 
magnitude. 



1 64 Familiar Talks on Astronomy y etc. 

Scotch. Well, so it would be with a comet if it 
should come in collision with the earth. It 
weighs but a few ounces at most, and it could 
not possibly hurt the earth. 

How do we know it weighs so little? Be- 
cause in 1776 a comet passed between Jupiter 
and its satellites. These satellites are small 
bodies, yet they were not at all disturbed in 
their orbits by the attraction of gravitation of 
the comet, while the comet, itself, was thrown 
entirely out of its course. 

While on this subject of comets and meteors, 
I must tell you I have given you the theory in 
relation to them that is generally accepted. 
We, doubtless, have much to learn concerning 
comets; and as to the origin of meteors, there 
are not wanting highly scientific men who be- 
lieve they were actually ejected into space by 
the volcanoes of the earth, in ages past. They 
are undoubtedly of volcanic origin. 

One remark more, and I have done with the 
stars. You know that people in the country 
who are without clocks can tell the time of day 
pretty well by the position of the sun. In 
former days, when clocks were rare and ex- 
pensive, most persons in the country had a 
" sun-mark," — that is, the shadow cast by the 
sun when on the meridian was marked so as to 
indicate noon. 

Now persons whose occupations keep them 



The Dipper, or Seven Stars. 165 

up at night, can judge of the time by the stars 
pretty accurately. Thus Poe says, — 

"And star-dials pointed to morn." 

In early times the " dipper " was the constel- 
lation most frequently observed, to judge of the 
time. 1 As I have told you, it is always visible 
to us. When I say this, I do not mean we see 
it in the day-time with the naked eye, — you 
know we do not, — but you must understand 
that in a telescope the stars can be seen in the 
day-time as well as in the night. 

The " dipper," or " seven stars," as some call 
it, moving round the pole, occupies all varieties 
of positions, as we have seen ; and it was natu- 
rally used to denote the hour of night. Thus, in 
" Henry IV.," Falstaff says, — 

"We that take purses go by the moon and seven stars." 

Now, the Pleiades are also called the seven 
stars, and Falstaff may have alluded to them; 
but I think he meant the " dipper," for in the 
same play the Carrier says, — 

*' An' it be not four by the day, I '11 be hanged ; 
Charles's Wain is over the new chimney ! " 

The "dipper" is sometimes called " Charles's 
Wain," in England, at the present day. It is 
from the Scandinavian Karlsvagn, — the Carle's 

1 In northern latitudes, of course. 



1 66 Familiar Talks on Astronomy, etc. 

Wain. It is called, also, " the wagon," from 
the Icelandic, Stori (great) Vagn. 

I said a few pages back I would explain what 
is meant by the precession of the equinoxes. I 
spoke of the effect, which is that the point of in- 
tersection of the ecliptic with the equator, — 
that is, the equinox, — moves backward very 
slowly and, as it were, meets the sun. Two 
thousand years ago this point was in the con- 
stellation Aries, and now it is in Libra. I called 
your attention to the fact that the signs of the 
Zodiac no longer corresponded with the Zodi- 
acal constellations, and must not be confounded 
with them. 

If the earth were a perfect sphere, there 
would be no precession; but it is an oblate 
spheroid, and the attractions of the sun and 
moon on the equatorial regions cause the pole 
of the equator to describe a very small circle 
round the pole of the ecliptic. Hence, though 
I have spoken of the earth's axis always point- 
ing in the same direction, it is not strictly true. 
The pole of the earth revolves about the pole of 
the ecliptic once in about 25,868 years. 

Astronomers have calculated that 4,500 years 
ago the pole-star was Alpha Draconis, and in 
about 12,000 years the pole-star will be the 
bright star Alpha Lyrce ; and although we are 
now nearer the sun in January, at one time we 



Precession and Nictation. 167 

were nearer it in June, and in the course of time 
will be again. 

The motion of precession is not uniform, 
owing to the varying attraction of the moon. 
This causes the pole to revolve in a wavy curve, 
and is called nutation. 



TALK THE ELEVENTH. 

Time. Its Measurement. Standard of Time. Apparent 
Solar Day. Sidereal Day. Mean Solar Day. Equa- 
tion of Time. Mean Time and Apparent Time. The 
Civil Day. The Astronomical Day. Lunar Day. 
Sidereal Time. Clepsydrae. Sun-Dial. Clocks and 
Chronometers. The Week. The Month. Lunar 
Month. Sidereal Month. Calendar Month. Tropical 
Month. Anomalistic Month. Nodical Month. The 
Year. Sidereal Year. Tropical Year. Anomalistic 
Year. Absolute and Relative Time. Local Time. 
Standard Time. 

THE subject of our next talk will be Time; 
and you will be surprised when I tell you 
that most persons know very little about it. I 
do not wonder at that myself, for in my experi- 
ence as a teacher at the U. S. Naval Academy 
and other colleges, I found this very subject of 
Time the most difficult one for the student to 
comprehend. And yet it seems a very simple 
matter. 

The exact measurement of time is one of the 
most important parts of practical astronomy. 
Let us see how we attempt to compass it. 

The natural standard of time is one revolution 
of the earth upon its axis. What we have to do, 



Time of Earth's Revolution. 169 

then, is to determine this period. We naturally 
turn to the sun to discover it. We are met with 
a difficulty at the beginning; and that is, that 
the intervals between the successive arrivals of 
the sun upon the same meridian are constantly 
changing. These intervals vary from about 24 
hrs. 16 min., to 23 hrs. 44 min. 

Now, as we cannot suppose the earth's motion 
on its axis to be irregular, we turn our attention 
to another celestial object, and see if the result 
is the same. We next, then, observe the moon ; 
the same irregularity in the intervals occurs. 
We then try the planets, and the result is the 
same. Lastly, we observe the stars, and the 
difficulty is solved. They, one and all, give 
always the same interval, and it never varies. 
The interval is 23 hrs., 56 min., 4 sec. All the 
stars give this result, and you know there are 
millions of them. The earth, then, makes one 
revolution upon its axis in 23 hrs., 56 min., 4 sec. 

Let us now look back and see why the sun 
gives irregular intervals. It is because the earth 
is moving around it. If the earth stood still in 
its orbit, the intervals would always be the same, 
and they would be the same as that given by 
the stars ; but owing to its yearly motion, the 
obliquity of the ecliptic, and the fact of its 
moving faster when in perihelion than when in 
aphelion, the intervals between the times of its 
meridian passage vary, as I have said. 



170 Familiar Talks on Astronomy, etc. 

In the case of the moon and planets, the rea- 
son is plain why they give irregular intervals; 
they have a motion of their own around the sun. 
And the moon, furthermore, revolves about the 
earth. The stars give always the same interval, 
because they are " fixed." 

Here, then, we have three days : the Apparent 
Solar Day (variable), the Apparent Lunar Day 
(variable), and the Sidereal Day (constant). 

Now the sun giving us what we call day and 
night, we must use it to determine our time. 
But no instrument, from a clepsydra to a clock, 
can be constructed to keep irregular intervals 
from twelve o'clock one day to twelve o'clock 
of the next. This is evident. What, then, do 
we do? Astronomers imagine what is called a 
mean sun, and suppose the revolution of the 
earth upon its axis to be performed in just 
twenty-four hours, and this is what we call a 
mean solar day. 

This is the time kept by our clocks and 
watches, and is our ordinary time ; that is, what 
is called mean time. A sun-dial shows the time 
by the true sun, and this time is called apparent 
time. The mean time is sometimes ahead of 
the apparent time, and sometimes behind it; 
but four times in the year, about April 15, June 
15, September 1, and December 24, the two 
times exactly agree. The difference between 
the apparent time and the mean time is called 



Equation of Time. 171 

the Equation of Time. It is never greater than 
about sixteen minutes. The apparent time can 
be changed to mean time by applying this 
" correction," and vice versa. The equation of 
time is given in the nautical almanac for every 
day of the year ; it is sometimes additive to the 
apparent time, and sometimes subtractive. 

But remember that the " time by the sun " 
is always apparent time. When we observe 
with an instrument the sun on the meridian it 
is twelve o'clock apparent time. If we calcu- 
late the time by observing the sun's altitude 
(which we do daily at sea, as I shall tell you 
of presently), it is the apparent time we find; 
and the apparent time is the same thing as the 
sun's hour angle if the hour is P.M., — because 
it is the number of hours from the meridian, 
or noon. If the hour is A. M., the apparent 
time subtracted from twelve, gives us the sun's 
hour angle. 1 

Mean time is the time kept by our clocks 
and watches, and is the time we allude to in 
daily life. When the mean sun is on the me- 
ridian it is twelve o'clock mean time; and our 
clocks and watches, if correct, indicate it. 

This mean solar day of twenty-four hours is 
called the Civil Day, and it commences at mid- 
night. It is reckoned through twelve hours, 

1 If we count our hour angle around the circle, the sun's 
hour angle is the apparent time. 



172 Familiar Talks on Astronomy, etc. 

only, to noon, and thence through another 
twelve hours to midnight, — and it is marked 
A.M. and P.M., as you know. 1 

Astronomers in their computations suppose 
the day to commence at noon, twelve hours 
after the commencement of the civil day; and 
this is called the Astronomical Day. It is prob- 
able this will be discontinued in a few years, 
and the civil day substituted. 

Now we have seen that the moon gives us 
irregular intervals for a day. A lunar day is 
longer than a solar day, as it should be; for 
the moon moves to the eastward while the 
earth is moving also from west to east. Hence 
it takes the earth more than twenty-four hours 
to " catch it up," as it were, and bring it upon 
the same meridian again. The mean lunar 
day is twenty-four hours, fifty-four minutes long. 
You see now why it is that the moon rises about 
fifty-four minutes later every night; and, also, 
why the flood tide makes about fifty-four min- 
utes later from day to day. 

1 S. Grant Oliphant says : " We have sixty divisions on the 
dials of our clocks and watches because the old Greek as- 
tronomer Hipparchus, who lived in the second century before 
Christ, accepted the Babylonian system of reckoning time — 
that system being sexagesimal. The Babylonians were ac- 
quainted with the decimal system, but for common or practical 
purposes they counted by sossi and savi, the sossos represent- 
ing sixty and the savos sixty times six — three hundred and 
sixty. 



The Sidereal Day. 173 

The sidereal day is always the same. We 
have, therefore, no mean sidereal day. In or- 
dinary life we have no use for sidereal time; 
indeed, perhaps there are but few persons who 
know anything about it But astronomers use 
it in their observatories. The hours on the 
face of a sidereal clock are marked up to 
twenty-four ; and it shows o hours O minutes o 
seconds when the vernal equinox, or a star 
whose right ascension is o hours o minutes o 
seconds, is on the meridian. We can change 
solar into sidereal time, and vice versa. 

As the sidereal day is shorter by about four 
minutes than the mean solar day, it follows that 
the stars rise four minutes earlier every night. 1 
The consequence of this is that in the course of 
a year we see all the stars visible at our place of 
observation. Since a star rises four minutes 
earlier daily, in a month of thirty days it will 
have gained one hundred and twenty minutes, or 
two hours, — that is it will rise two hours earlier. 
In six months it will have gained twelve hours, 
— so that a star which was rising, say at sunset, 
will in six months be just setting; while the 
star that was setting at that time will be rising. 
Thus you see that in the following six months 
we shall have an entirely new set of stars above 
the horizon at night. You see that if the side- 
real day was of the same length exactly as the 
1 See note, page 179. 



174 Familiar Talks on Astronomy, etc. 

mean solar day, the same stars would be visible 
every night; one half of them would be above 
the horizon at night, and the other half in the 
daytime, and the latter would be visible only 
in a telescope. Of course this does not apply 
to the circum-polar stars, which you know do 
not set; but are always above the horizon. 
The constellation of the Great Bear, or " Dipper," 
is an example. 

For the measurement of time the ancients 
used clepsydra, and sun-dials. The clepsydra 
were, as the name denotes, water-clocks. That 
is, the intervals of time were measured by the 
flow of water. If we take an ordinary hour- 
glass and fill it with water instead of sand, it 
will represent a clepsydra. When in use they 
were constructed of various forms, — all de- 
pending, however, upon the flow of water, — 
and were made ornamental as well as useful; 
just as our parlor clocks are at the present time. 
Suppose we should make a rectangular box, 
fill it with water, and then bore a small hole 
in the bottom to allow the water to escape. 
Now, we could see how much water ran out 
in one hour, and could mark the box by draw- 
ing a horizontal line; then, supposing the 
box to be in exact proportion, twelve of these 
horizontal lines represent twelve hours. The 
box would have to be filled with water at the 



Clepsydra. 175 

end of that time, just as we have to wind up 
our clocks and watches. 

I have seen a drawing of a clepsydra which 
represented the figure of a man standing upon 
a flat piece of wood, floating on the top of 
water in a box. The man was in armor, and 
held a drawn sword in his right hand. The 
point of the sword rested on a perpendicular 
dial, upon which were marked the numbers 
from one to twelve. When the box was full 
of water, the sword pointed to twelve ; in the 
course of an hour, the water having fallen, the 
sword pointed to one, and so on. You see, then, 
the construction admits of a variety of forms. 

But you will naturally ask me how these 
marks were determined. As the ancients had 
no clocks, how did they know the interval we 
call an hour? Well, they did not know it. They 
called the time from sunrise to sunset 12 hours, 
and marked their clepsydrce accordingly. It fol- 
lowed from this that as the days in the summer 
are longer than in winter their hours were 
of different lengths; and the winter clepsydra 
would not answer for summer, and vice versa, 
In fact, except for measuring intervals of time, 
they were very inaccurate, unless different ones 
were used at different seasons of the year. 

The sun-dial was used by the Jews as long 
ago as 742 B. c. It was a great improvement 



176 Familiar Talks on Astronomy, etc. * 

on the clepsydra; but, you know, in cloudy 
weather and at night it is useless. The con- 
struction of a sun-dial is very simple ; it consists 
of a style and a dial. The style is a rod, set 
parallel to the earth's axis, and its shadow is 
thrown upon the dial, which latter is marked to 
indicate the hours. You will find frequent refer- 
ence to the sun-dial in Shakspeare, and other 
old poets; and if you ever visit the Spanish 
countries of this continent, you will find in every 
town of importance a sun-dial, which was placed 
there by the Conquerors. One of the most 
interesting objects in the town of Acapulco, 
Mexico, is the old sun-dial in the plaza. 

Mr. Lockyer says : " Clocks appear to have 
been first used in Europe in the eleventh cen- 
tury; and the first clock made in England was 
in 1288." 1 

1 Shakspeare says, — 

"And then he drew a dial from his poke, 
And looking on it with lack-lustre eye, 
Says, very wisely, ' It is ten o'clock.' " 

Bulwer says : " Clockwork appears to have been introduced 
into England in the reign of Edward III. [1327-77], when three 
Dutch horologers were invited over from Delft. They must 
soon have passed into common use, for Chaucer [1320-1400] 
thus familiarly speaks of them : — 

" ' Full sickerer was his crowing in his loge, 
Than is a clock or any abbey orloge.' " 

Chambers'i Etui. 



The Week. 



177 



Now, both clocks and watches are in use all 
over the civilized world, and are sold so cheap 
that we rarely find a house without one. The 
sidereal clock used in observatories, and the 
chronometer used by navigators are made with 
great care, and are still expensive instruments. 
I will tell you something about chronometers, 
and their use, in another place. 



The week} unlike the day, month, and year, 
is not connected with the movement of any 
heavenly body. Mr. Lockyer says the names of 
the seven days of the week were derived by the 
Egyptians from the seven celestial bodies then 
known ; and that the Romans, in their names 
for the days, observed the same order, distin- 
guishing them as follows, — 



Dies Saturni, 
Dies So/is, 
Dies Limce, 
Dies Martis, 
Dies Mercurii, 
Dies Jovis, 
Dies Veneris, 



Saturn's Day, 
Sun's Day, 
Moon's Day, 
Mars's Day, 
Mercury's Day, 
Jupiter's Day, 
Venus's Day, 



Saturday. 

Sunday. 

Monday. 

Tuesday. 

Wednesday. 

Thursday. 

Friday. 



We see at once the origin of our English 
names for the first three days; the remaining 

1 I think it likely that the ancients were led to this division 
of time by counting from new moon to first quarter (and so on) 
of the moon. They divided the lunar month into four parts ; 
but this is only a supposition. 



178 Familiar Talks on Astronomy, etc. 

four (Mr. Lockyer says) are named from Tiw, 
Woden, Thor, and Frigga, Northern deities 
equivalent to Mars, Mercury, Jupiter, and 
Venus, in the classical mythology. 

The month is a period regulated entirely by 
the moon's motion around the earth. The lunar 
month is reckoned from new moon to new 
moon; its length is about 29 days, 12 hours. 
The sidereal month is the interval between two 
successive conjunctions of the moon with the 
same fixed star; it is, in fact, the exact time it 
takes the moon to make one revolution about 
the earth. Its length is 27 days, 9 hours. 

The calendar month is the month recognized 
in the almanacs ; such as January, February, 
March, etc. You know the number of days in 
each of these months. 

Astronomers speak also of the tropical 
month, 1 the anomalistic month, and the nodical 
month; but I need not dwell upon these dis- 
tinctions here. 

We next come to the year. This is the time 
of the earth's revolution about the sun. There 

1 The tropical month is the revolution of the moon with 
respect to the movable equinox. The anomalistic month is 
the time in which the moon returns to the same point — such 
as the perigee or apogee — of her movable elliptic orbit. The 
nodical month is the time in which the moon accomplishes a 
revolution with respect to her nodes, the line of which is also 
movable. 



Sidereal and Tropical Year. 179 

are various years, just as there are different 
kinds of days and months. 

The time that elapses between two successive 
conjunctions of the sun (as seen from the earth) 
with a fixed star, is called a sidereal year; its 
length is 365 days, 6 hrs. 9 min. 9.6 sec, — and 
this is the exact time of the earth's revolution 
about the sun. 1 

The time that elapses between two successive 
passages of the sun through the vernal equinox, 
is called the solar, or the tropical year. Its 
length is 365 days, 5 hrs. 48 min. 46 sec. It is 
rather less than the sidereal year, because the 
equinox has moved a little to the westward, and 
the sun reaches it a few minutes before it reaches 
the star. This movement is known as the pre- 
cession of the equinox, as I have said. 

If we consider the time it takes the sun to 
move from perihelion to perihelion again, we 
have still another year ; it is called the anomal- 
istic year. Its length is 365 days, 6 hrs. 13 min. 
4.9 sec. It is about 4 minutes longer than the 
sidereal year, because these points (aphelion and 
perihelion) have a slight forward or easterly 
motion, and it takes the sun a little longer to 

1 That is, reckoned in solar time. It should be observed that 
in 365 solar days the earth revolves upon its axis 366 times. 
We have seen that the stars gain about 4 minutes a day. 
Roughly, we have 4 minutes multiplied by 365 = 1,460 
minutes = 24 hours ; so 365 solar days equal 366 sidereal 
days. 



180 Familiar Talks on Astronomy, etc. 

reach them. The line joining the aphelion and 
perihelion points is called the line of apsides. 

But the year we are interested in is the solar 
or tropical year, because on it depends the 
change of the seasons ; and we may disregard 
the sidereal and anomalistic years. When I 
speak of a year hereafter, I mean the solar or 
tropical year. 

Having once determined the exact length of 
the year, astronomers were enabled to correct 
the calendar, as I explained to you in our first 
talk. 

Time, then, is regulated by the sun. When 
the real sun is on the meridian of any place it 
is twelve o'clock, apparent time, at that place; 
and a sun-dial will indicate twelve hours. When 
the mean sun is on the meridian of any place it 
is twelve o'clock, mean time, at the place ; and 
our watches and clocks indicate it. You see it 
is twelve o'clock at every place on the earth's 
surface when the sun is on the meridian of that 
place. But the sun must cross the meridian of 
all these places at a different time. How, then, 
can it always be twelve o'clock? I must explain 
this, as it leads up to the difference between ab- 
solute time and relative time, which I wish you 
clearly to comprehend. 

Let us take Greenwich, which, as we are in 
about 75? west longitude, is five hours ahead of 



Relative and Absolute Time. 181 

us in absolute time. As the earth turns upon its 
axis, or moves 360 , in twenty-four hours, it must 
move 1 5 in one hour; and as it turns from west 
to east, the absolute time of a place east of us, 
as Greenwich, must be faster than ours, or in 
advance of ours. Now as we are in longitude 
75 west of Greenwich, the time at Greenwich is 
five hours in advance of ours. The longitude of 
a place is simply the difference between its time, 
and the time at Greenwich, reckoning longitude 
from that place ; so if I say we are five hours 
from Greenwich, it conveys the idea that we are 
in longitude 75 °. If I say our time is five hours 
faster than Greenwich time, I indicate that the 
longitude is 75 east; and if I say our time is 
five hours behind Greenwich time, I indicate 
that the longitude is 75 ° west. 

Now the sun crosses the meridian of Green- 
wich at twelve o'clock, and it crosses our merid- 
ian at twelve o'clock ; the relative times are the 
same ; but in absolute time, the sun crosses the 
meridian of Greenwich five hours before it does 
ours. When it is twelve o'clock local time at 
Greenwich, it is 7 A. M. here by our local time. 
When it is twelve o'clock here by our local time, 
it is 5 P. M. at Greenwich by its local time. 

Every place has its own local time ; and when 
the mean sun is on the meridian of any place, 
the clocks mark twelve hours at that place. 
This comes from a law of Nature, — the earth 



1 82 Familiar Talks on Astronomy \ etc. 

in its revolution must bring the meridian of 
every place under the sun, once in twenty-four 
hours ; and this moment we have agreed to call 
twelve o'clock, and it is the natural initial point 
of our day (meaning, of course, twenty-four 
hours). 

Let me give you another illustration to show 
the difference between absolute and relative 
time. The time of the sun's rising at any place 
depends upon the latitude of the place, and the 
sun's declination. We can construct a table by 
assuming all latitudes from o° to 90 , and all 
declinations from 0° to 23 J^°, and calculating the 
time of sunrise for every degree of latitude, and 
every degree of declination. Such a table is in- 
serted in our books on navigation, and the navi- 
gator has only to enter it with his latitude and 
the declination of the sun to find the hour of 
sunrise. It saves him the trouble of computing 
it. The time found is the apparent time ; and 
as the navigator at sea keeps apparent time, it 
suits him as it is. If we, here on shore, find this 
time, we apply the equation of time to it, and 
we have the mean local time of sunrise. 1 

The sun rises at the same hour to every ob- 
server on the surface of the earth in the same 
latitude. 



1 Knowing the time of the sun's rising, we have of course 
the time of its setting ; it is twelve hours minus the time of 
rising (that is, if we keep local time). 



Standard Time. 183 

For example : Gibraltar is in about the same 
latitude as Norfolk, but the difference of longi- 
tude is about yo° ; that is, the difference of time 
is 4 hrs. 40 min. Now on, say the 1 st of May 
the sun rises at Norfolk at 6.45 A.M., apparent 
time. It rises also at Gibraltar at .6.45 A. M., 
apparent time. That is, the relative times are 
the same ; but in absolute time the sun rises 4 
hrs. 40 min. sooner at Gibraltar than at Norfolk. 

I have dwelt upon this subject of time for the 
reason that in 1884-85 a change was made in 
the United States in its reckoning. We have 
discarded " local " time, and have decided to 
use the time of some other meridian. We call it 
" Standard " time. Thus, all places between the 
meridians of 6y}4° and 82*4° (that is, between 
the longitudes 67 30', and 82 30'), use the 
time of the 75th meridian, — the mean meridian 
between them; all places between 82^° and 
97^° use the time of the 90th meridian; and 



1 Professor A. Hall, of the U. S. Naval Observatory, Wash- 
ington, wrote me in relation to the adoption of "standard 
time : " "I believe it will lead to all manner of absurdities." 

I find the following despatch in the " Baltimore Sun " of 
Feb. 22, 1889: — 

Bellaire, O., Feb. 21. — The question of time in Bellaire 
has been unsettled for some time. The Board of Education 
has been running the clock in the tower of the Central School 
building on Eastern standard time. The council wanted sun 
time, and finding the board would not change, passed an ordi- 



184 Familiar Talks on Astronomy, etc. 

I believe we have made a mistake in adopting 
this rule, for the reason that we are legislating 
against a natural law. I think the time at a 
place should be indicated by the sun's passage 
across the meridian of that place, which, as 
I have before said, is the initial point of the 
day. 

I believe, moreover, we are confusing a sub- 
ject already sufficiently complicated. Let us 
consider a few points. 

I see by the atlas that a place called Lancas- 
ter, in Ohio, is in about the longitude 82 30' W. 
from Greenwich. If the main street of that town 
runs north and south, and if the centre of that 
street is in exactly 82 30' west longitude (as it 
may be), a man changes his time one hour by 
simply crossing the street. The citizens east of 
the street keep the time of the 75th meridian, 
and those west of it the time of the 90th merid- 
ian, which times differ one hour. And whether 
this meridian of 82^° runs through a town or 

nance making it an offence for any person to expose a time- 
piece in any public place showing any other than meridian 
time. Then the war began, and legal counsel was secured by 
both sides. 

Meanwhile the people were divided on the question ; some 
using one time, some another, and others still going by railroad 
time. To-day the matter culminated in the arrest of M. Hoff- 
man, Wm. Burgenthal, James T. Kelly, and G. W. Yost, mem- 
bers of the Board of Education, — the other two members 
escaping, as they had become reconciled to sun time. The 
case is set for Monday, and an interesting fight is promised. 



Standard Time. 185 

not, there must be places within a short distance 
of each other whose times differ one hour if the 
rule is adhered to. 

Again, suppose a man in longitude 82 , 29/, 
30", looks in the table to find the time of sunrise 
on the 2 1 st of March. He finds that the sun 
rises at 6 A. M. and sets at 6p.M.; but according 
to his clock, which is set to the time of the 75th 
meridian, the sun rises at 6.30 A. M. and sets at 
6.30 P.M. That is, it rises 55^ hours before 
noon, and sets 6^4 hours after noon. Will he 
not find it difficult to explain to his children 
this anomaly? 

I could give many more examples of the 
kind ; but as the adoption of the time is un fait 
accompli, perhaps I have said enough. My ob- 
ject in introducing it is to induce you to think 
of the matter. 1 

We frequently see in the papers a notice of 
the running time of a steamer between Liver- 
pool and New York. Liverpool is in longitude 
3 west, and New York in longitude 74 west. 
The difference of longitude is 71 , and the dif- 
ference of time is 4 hrs., 44 min. Suppose a 
steamer to leave Liverpool on Monday at noon 

1 Since writing this I see in the " San Francisco Bulletin " 
the following : " Standard time is being abandoned in some 
Michigan cities and towns, and it is thought the Legislature of 
that State will repeal the law that legalized its adoption." 



1 86 Familiar Talks on Astronomy, etc. 

(local time), and to arrive at New York the fol- 
lowing Monday at noon (local time). Her run- 
ning time would not be seven days. It would 
be 7 days, 4 hrs., 44 min., because when it is 
noon at New York, it is 4 hrs., 44 min. past noon 
at Liverpool. 

Again, suppose a steamer to leave New York 
on Monday at noon, and to arrive at Liverpool 
the following Monday at noon. Her running 
time would be 6 days, 19 hrs., 16 min., because 
when it is noon at Liverpool, it is 7 hrs., 16 min. 
A. M. at New York. In the first case, as the 
steamer goes westward or from the sun, her 
days are longer than twenty-four hours ; in the 
second case, going eastward she meets the sun, 
and her days are less than twenty-four hours. 

The papers are accustomed to call this cor- 
rected time the steamer's mean running time. 
It is not the mean running time at all. It is the 
exact time in which she has crossed the ocean 
in days of twenty-four hours long. 



TALK THE TWELFTH. 

International Conference held at Washington for the 
Adoption of a single Prime Meridian and a Universal 
Hour, October, 1884. Explanation of the Method by 
which Navigators adjust their Time when circumnavi- 
gating the Globe. 

IN 1884, at an International Conference held 
at Washington to decide upon the adoption 
of one " prime meridian " for the world, one of 
the subjects discussed was the propriety of 
adopting one " time " for all nations. This Con- 
gress was called by the President of the United 
States, and twenty-six countries were represented. 
Among the delegates were the Directors of the 
Observatories of Washington, Cambridge (Eng- 
land), Paris, Rio de Janeiro, and Mexico; and 
distinguished astronomers and hydrographers 
from all parts of the world. The following 
proposition was adopted : — 

"The Conference proposes the adoption of a uni- 
versal hour for all the uses for which it may be found 
convenient, and which will not prevent the use of the 
local hour or any other normal hour which may seem 
to be desirable." 



1 88 Familiar Talks on Astronomy, etc. 
And also this : — 

" The universal day should be a mean solar day. 
It should commence, for the entire world, at the begin- 
ning of mean midnight at the first meridian [Green- 
wich], agreeing with the commencement of the civil 
day and the date of this meridian, and it should be 
counted from o to 24 hours." 

I think it would have been better to have 
confined this discussion to the observatories of 
the world. Astronomers understand this sub- 
ject of time, and can readily come to an agree- 
ment as to a universal day and hour. The 
world generally know little about it. An at- 
tempt to introduce it and to have two dials on 
our clocks, as some propose, will, I believe, lead 
to endless vexation, if not confusion. 

All change is not necessarily progress. Al- 
though a little in advance of my subject (for I 
intend to tell you a good deal about longitude), 
I will say something as to the action of this 
Congress on the adoption of one prime meridian 
for all nations. 

You know we reckon our longitude from 
Greenwich; and, indeed, it was stated in the 
Conference that seven tenths of the nations of 
the earth reckon longitude from the same meri- 
dian. France reckons from Paris, Spain from 
Madrid, Brazil from Rio de Janeiro ; and a few 
other countries reckon from their capital cities. 



The Prime Meridian. 189 

It is a mere arbitrary rule; we can reckon longi- 
tude from any meridian we choose to select. 
We naturally took the meridian of Greenwich, 
where there is one of the best and oldest observ- 
atories in the world. We use English charts 
and it is convenient to reckon our longitude 
from Greenwich. 

When the question of adopting one prime 
meridian for the world was presented to the 
Conference, it was a grave one, and its impor- 
tance was duly appreciated. As might have 
been expected, the first motion made was to 
adopt the meridian of Greenwich ; and equally 
of course, France objected. Let us see why. 
If France had consented to change her meridian, 
all her charts would have had to be eventually 
issued anew, the plates renewed, and all her 
school atlases republished. The cost to her 
would have been millions of dollars. But this 
is not all ; and the point I am about to call 
your attention to was not — singular to say — 
alluded to by any delegate to the Congress. 
At least, I do not find any reference to it in the 
printed proceedings. 

Astronomy teaches us how to regulate time, 
calculate eclipses, and many other useful things ; 
but I am of the opinion that its greatest useful- 
ness is that it enables us to find our way across 
the oceans of the world, and bring nations into 
communication. To read the proceedings of 



190 Familiar Talks on Astronomy, etc. 

the Congress one would think navigators were 
not interested in the prime meridian. The dis- 
cussion was so highly scientific that the practical 
was scarcely alluded to. 

Many navigators know but little of the science 
of navigation, or theoretical navigation. They 
understand the practice ; and know how to find 
the position of a ship, and to shape a course. 
The books on navigation give rules for finding 
the latitude, longitude, etc. ; and these rules are 
made so plain and practical that any man of 
ordinary education can follow them. Many 
captains can find the latitude and longitude, and 
yet cannot explain the principle. 

Now suppose you change the meridian from 
which he is accustomed to reckon. You con- 
fuse him, and he has to learn his rules over 
again ; and while he is doing so, shipwrecks in- 
crease in number. If we should change our 
meridian, and reckon longitude from Washing- 
ton, marine insurance would probably go up one 
hundred per cent. 

On the proposition to adopt the meridian of 
Greenwich, twenty-one countries voted in the 
affirmative, one in the negative, and France and 
Brazil declined to vote. That is, the countries, 
generally, using the meridian of Greenwich ad- 
hered to it, and those using the meridian of Paris 
declined to make a change. All of which might 
have been foreseen before the Congress met. 



The Prime Meridian. 191 

It is true France proposed and was willing to 
adopt what she called a " neutral " meridian ; 
but as that would have caused all nations to 
make a change, it was very wisely rejected. 

One argument in favor of the adoption of 
one prime meridian was that in the case of 
a ship at sea exchanging longitudes with an- 
other, she was sometimes in doubt as to 
whether the longitude shown was from Green- 
wich or Paris; but it is usual to ask, when in 
doubt. 

French charts are sometimes used by our sea- 
men, though the longitudes are reckoned from 
Paris. As we know Paris is in longitude 2° 20' 
east of Greenwich, we have simply to apply 
this to our mode of reckoning, in marking a 
ship's position on the chart. We can use any 
chart. It does not matter what meridian the 
longitude is reckoned from ; all we want to 
know is the longitude of that meridian east or 
west of Greenwich. 

The proposition before the Conference, to 
reckon longitude round the world from o° to 
360 was voted down. I was glad to see it; and 
must repeat that I see no good reason why we 
should change our time or longitude. We have 
north and south latitude, east and west longi- 
tude, and A. M. and P. M. time. 

The only change I see reason for is to 
change the Astronomical Day to the Civil Day ; 



192 Familiar Talks on Astronomy, etc. 

and this should be prospective. We cannot 
change it at once without producing confusion. 
The Nautical almanac is computed for five or 
six years ahead, using the Astronomical Day. 
This change might be decided by astronomers, 
and a certain day and year selected in which 
to begin the change — say January 1, 1895. 
After that date, the Astronomical Day would 
be disregarded and the Civil Day substituted 
in the calculations for the Nautical Almanac ; 
and the change should be frequently alluded to 
in the newspapers, so that the attention of navi- 
gators would be called to it, and they would 
be prepared for it. 

I see marked on some school atlases the 
" longitude from Washington." The sooner this 
is discontinued, the better. As I said in the last 
talk, people, generally, know very little about 
either time or longitude. The more reason, then, 
why we should hesitate to make any change in 
them. 

When I was commanding a steamer of the 
Pacific Mail Steamship Company, in the Pacific, 
I was frequently asked by my passengers why it 
was that, in going to China from San Francisco, 
the navigator "dropped" a day in his reckoning 
at the 1 80th meridian, while in going to San 
Francisco from China he " repeated " a day. 
This I will try to explain. 



Circumnavigating the Globe. 193 

The earth turns upon its axis, from west to 
east, once in 24 hours. It follows, then, that a 
man travelling round the world in an easterly 
direction makes one more revolution about the 
earth's axis than a man who remains at the 
starting point. He therefore reckons one day 
more in his account. Not that he has lived any 
longer than the stationary man ; he makes it 
one day more, but as he constantly meets the 
sun, his days are shorter, and are less than 24 
hours. 

Similarly, a man travelling round the world in 
a westerly direction makes one revolution less 
about the earth's axis than the man who re- 
mains at the starting point. He therefore 
reckons one day less in his account. In this 
case he travels from the sun, and his days are 
longer, and more than 24 hours. 

Let us suppose two men, A and B, to be at 
Greenwich. B remains at home, and A travels 
round the world, at a uniform rate, in an easterly 
direction. Let us suppose A to go round in 24 
of his own days. He must, then, travel 15 
degrees in each one of his days; that is, he 
gains one hour of time each day. When he 
arrives at Greenwich he will find that by B's ac- 
count he has been gone but 23 days. The 
actual time of both is, of course, the same. A 
reckons 24 days, of 23 hours each ; B reckons 
23 days, of 24 hours each. 
13 



194 Familiar Talks on Astronomy, etc. 

Again, let us suppose two men, B and C, to 
be at Greenwich. B remains at home, and C 
travels round the world, at a uniform rate, in a 
westerly direction. Let us suppose C to go 
round in 24 of his own days. He must travel 
15 degrees in each one of his own days; and, as 
he travels from the sun, each one of his days 
will be 25 hours long. When he arrives at 
Greenwich, he will find that by B's account he 
has been gone 25 days. C reckons 24 days of 
25 hours; B reckons 25 days of 24 hours, — the 
same thing. 

Now, let us suppose the three men, A, B, and 
C, to be at Greenwich. A goes round the world 
in an easterly direction ; C goes round in a 
westerly direction ; and B remains at home. It- 
does not matter how fast A and C travel; but 
suppose they arrive at Greenwich on the same 
day, and let that day be, by B's account, Sun- 
day. By A's reckoning it is Monday, and by 
C's reckoning it is Saturday. A has gained a 
day, and C has lost one. They differ from B 
one day, and from each other two days. It is 
on this that Edgar Poe founded his story en- 
titled, " Three Sundays in a Week; " and Jules 
Verne uses it in his "Around the World in 
Eighty Days." 

The first circumnavigators reckoned in this 
way; and so it was that Magellan's companions, 
travelling westward, were one day behind in 



Mage I la n 's Voyage. 195 

their reckoning upon their return home. They 
stopped at Santiago, Cape de Verde islands, 
and there the navigators first learned of their 
being one day behind in their account. It is a 
curious fact that they put to sea suddenly to 
avoid being detained by the Portuguese authori- 
ties, just as Columbus did from Lisbon upon his 
return from his first voyage. When Sebastian 
del Cano — who had succeeded to the command 
of Magellan's ship — announced that he had 
sailed around the world, it was at first not be- 
lieved in Spain ; but to the learned the fact that 
he was one day behind in his reckoning was 
proof that he had circumnavigated the globe by 
sailing in a westerly direction. 

It was not long after the first circumnaviga- 
tions that astronomers devised a method by 
which this confusion of dates might be avoided ; 
and that was to correct the reckoning of time at 
the 180th meridian. 

Ships sailing round the world in an easterly 
direction, "repeat" a day when they reach the 
meridian of 180 ; and those sailing round in a 
westerly direction, " drop " a day at the same 
meridian. 

I must call your attention to the fact that if 
we drop a day, that is, omit a day, in our 
reckoning, we put our time ahead 24 hours ; and 
if we repeat a day, we put our time behind 24 
hours. It is necessary you should comprehend 



196 • Familiar Talks on Astronomy, etc. 

this; and you must observe that we can only 
correct our time by 24 hours, as otherwise we 
would turn day into night. 

Now, a ship, A, sailing eastward, is, when she 
arrives at the 180th meridian, 12 hours ahead of 
Greenwich time; if she keeps on, without cor- 
recting her time, she is, upon her arrival at 
Greenwich, 24 hours ahead, as we have seen. 
But at the 180th meridian, where she is 12 hours 
ahead, she repeats a day, and this puts her time 
12 hours behind Greenwich. By the time she 
arrives at Greenwich she will have gained the 
12 hours she put herself behind, and her day 
and time will be the same as Greenwich. If, for 
example, she crosses the 180th meridian on 
Thursday, she calls the next day Thursday, 
also; and remember she passes from east to 
west longitude. 

A ship, C, sailing to the westward is, when 
she arrives at the 180th meridian, twelve hours 
behind Greenwich time ; and if she keeps on 
without correcting her time, she is, upon her 
arrival at Greenwich, twenty-four hours behind, 
as we have seen. But at the 180th meridian, 
where she is twelve hours behind, she drops a 
day, and this puts her time twelve hours ahead 
of Greenwich. By the time she arrives at Green- 
wich she will have lost the twelve hours she put 
herself ahead, and her day and time will be the 
same as Greenwich. If, for example, she crosses 



Circumnavigating the Globe. 197 

the 1 80th meridian on Wednesday, she calls the 
next day Friday ; and she passes from west to 
east longitude. 

If the two ships, A and C, meet at the 1 80th 
meridian, they differ in time twenty-four hours. 
A calls it Thursday, C reckons it Wednesday. 
When they correct their times, as just explained, 
they, in point of fact, interchange dates. Thus, 
A calls the next day Thursday, and C calls it 
Friday. 

This is the way in which navigators correct 
their date. I have supposed the ships to sail 
from Greenwich for the sake of illustration. Of 
course it matters not what port they sail from. 

You see now, I hope, why a navigator in going 
from San Francisco to China drops a day at the 
1 80th meridian. He thus changes his date to 
the China date. When he returns to San Fran- 
cisco from China he repeats a day, and thus 
changes back again to San Francisco time. 



TALK THE THIRTEENTH. 

Nautical Astronomy. Astronomical Instruments. The 
Transit Instrument. The Meridian Circle. The Prime 
Vertical. The Mural Circle. The Equatorial Instru- 
ment. The Nautical Almanac. The Early Naviga- 
tors. The Mariner's Compass. Voyage of Columbus. 
The Trade- Winds. The Sargasso Sea. Variation of 
the Compass. 

THE plan of this work would not be com- 
plete without a few words on what is 
called nautical astronomy, or astronomy as ap- 
plied to the science of navigation. When we 
consider that by its aid the sailor is enabled to 
find his way across the trackless ocean, we can 
appreciate one of the practical benefits of the 
science of astronomy. 

I am the more inclined to say a few words on 
this subject from the fact that most persons are 
entirely ignorant of it. It has been in my expe- 
rience to serve on board men-of-war carrying 
abroad ministers to foreign countries, — men of 
scholarly attainments, but who had never before 
left their native shores, — and I well recall their 
expressions of surprise and wonder when, after 
a voyage of fifty or sixty days, the destined port 



The Transit Instrument. 199 

was seen right ahead. I have also when in the 
merchant marine carried thousands of passen- 
gers between the ports of Panama and San 
Francisco, — I have, indeed, " surveyed mankind 
from China to Peru," and have had occasion to 
observe the same ignorance in relation to the 
science of navigation. 

When the " captain " takes his observations 
for the determination of the latitude and longi- 
tude, the majority of the passengers regard it as 
some mystic operation. Now, although it re- 
quires years and experience to make a really 
good navigator, yet the principle by which a 
ship's position is found at sea is very easy to 
comprehend, and every one should know it. I 
purpose in this and the succeeding talk to 
explain it, in as simple language as I can 
command. 

Before entering upon the subject, let us see 
what astronomers are doing in their observa- 
tories, and glance at some of the instruments 
they are using. 

A telescope is an astronomical instrument; 
or perhaps we had better say, it is the " sight " 
attached to fundamentally different instruments. 
The Transit Instrument is a telescope mounted 
so that, as it turns upon its axis, it describes the 
plane of the meridian. The axis points east 
and west. When the telescope is horizontal it 
points due north or south. It can be revolved 



200 Familiar Talks on Astronomy, etc. 

upon its axis from north to south, and its use is 
to determine the right ascensions of the heav- 
enly bodies, and their transits. By " transit " is 
meant the passage of a body across the merid- 
ian, or its culmination, as it is also called. 

The telescope of the transit instrument cannot 
be pointed either to the right or left, and its use 
is limited to the observation of heavenly bodies 
when on the meridian. This is only a very 
short interval of time; the object enters the 
field of the glass on one side, and in a few sec- 
onds disappears on the opposite side. 

If we attach a graduated circle to the axis, at 
right angles to it, we can measure the decli- 
ation of a celestial body, or we can measure its 
meridian altitude. It is then called a Meridian 
Circle. This instrument is sometimes mounted 
so that its axis points north and south. The 
telescope then points due east and west; and 
the instrument is called a Prime Vertical, for the 
reason that the telescope, when revolved upon 
its axis, moves in the plane of that circle of the 
celestial sphere called the prime vertical. 

The Mural Circle is the same as a Meridian 
Circle in its use. The mounting is different. 
The horizontal axis is supported at one ex- 
tremity only, and this extremity is let into a 
stone wall; hence, mural, from murus, a wall. 
It is not so accurate an instrument as the Me- 
ridian Circle, as we cannot reverse it in deter- 



The EqiLcitorial Instrument. 201 

mining its error, and its use has been nearly 
abandoned. 

The Equatorial Instrument is mounted so that 
its main axis points to the poles of the heavens. 
It carries two circles, one of which is called the 
hour circle, and the other the declination circle. 
By means of a clock-work arrangement the tele- 
scope is made to revolve upon its polar axis 
once in a sidereal day. We see, then, that hav- 
ing once set it upon a star, it follows that star 
from its rising to its setting, and has it in view 
always at the same point in the focus of the 
object glass. The telescope revolves in a direc- 
tion contrary to the motion of the earth on its 
axis. 

This is the instrument used by the astronomer 
who wishes to observe a celestial body for a 
long time, to study its physical constitution, 
etc. 

Astronomers use also Zenith Sectors, Alt- 
azimuths, and some other instruments which it 
is not necessary to describe. 

Now, while some observers are engaged in 
studying the physical constitution of the heav- 
enly bodies, fixing the positions of the stars, 
calculating eclipses, etc., others are at work 
on the necessary calculations to be inserted in 
a book called the " Nautical Almanac," or 
the Ephemeris y a book especially designed for 
the use of navigators. In this book we find the 



202 Familiar Talks on Astronomy, etc. 

right ascension and declination of the sun, 
moon, planets, and principal stars. We find, 
also, the apparent semi-diameters of the sun and 
moon, the Equation of Time, and, indeed, all 
that is useful to the navigator in determining 
his position at sea. 

Not only that, but these elements are calcu- 
lated for years ahead ; so that when a ship sails 
on a three years' cruise, the navigator is pro- 
vided with nautical almanacs for four or five 
years in advance. 

Let us now glance at the early navigators. 
Our books say the Phoenicians were the earliest 
navigators; but we know almost nothing con- 
cerning the early voyages of the Chinese, and 
other Eastern nations. One thing is certain: 
they kept near the shore. In the voyages of 
Saint Paul we read that, on his last voyage from 
Cesarea to Rome, his ship coasted along the 
shores of Asia Minor, until it was driven 
off by the fury of a tempest, and finally 
wrecked on the island of Melita, or Malta, as 
is supposed. 

Why did the early seamen keep near the 
shore? Because they had no compass. 

Most of the ancients knew that loadstone 
attracted iron ; and it must have been soon dis- 
covered that a piece .of iron rubbed on a load- 
stone becomes a magnet, and will attract other 



Polarity of the Needle. 203 

pieces of iron, and will, moreover, point to the 
north when freely suspended. 1 

Some writers assert that this was Gioja's dis- 
covery; but it is said the Chinese had, in Marco 
Polo's time [a. D. 1265], on the northern confines 
of their country, magnetic needles suspended to 
point out the way to travellers coming from the 
north. I have sometimes thought it was in this 
way the Chinese happened to mark the south 
point of their compass cards, as we do the north 
point. 

I have read an account written by a French 
gentleman who, somewhere about the eleventh 
century, made a voyage in an Arabian ship 
from one port in the Mediterranean to another. 
He relates that, the sky being overcast, the 
captain placed a piece of iron on a cork, floated 
it in a basin of water, and carefully observed the 
direction in which it pointed. 

Other writers assert that Roger Bacon, in the 
thirteenth century, discovered the polarity of 
the needle. But at all events, we see the mere 
fact that a needle, floating in a basin of water, 
would point to the north, was of very little prac- 
tical use to the first navigators. When the 
weather was clear they steered by the sun by 
day, and the stars by night. 

1 Dr. Johnson says : " The lode-star is the leading, or 
guiding, star ; that is, the pole-star. The magnet is for the 
same reason called the lode-stone, — either because it leads iron, 
or because it leads the sailor." 



204 Familiar Talks on Astronomy, etc. 

The weight of testimony goes to show that 
the mariner's compass was discovered, or in- 
vented, by Flavio Gioja, in the early part of the 
14th century. He was a native of Amalfi, a 
small town near Naples ; and the mariner's 
compass being of all the instruments used by 
navigators the most useful, 1 I will proceed to 
describe it. 

It consists of a Needle, a Card, and a Bowl. 
The card is circular, and is divided into 32 equal 
parts, called points, and these points are also 
divided into halves and quarters. Since the 
circumference of a circle contains 360 , each 
point equals 11° 15'. The Cardinal Points are 
north, south, east, and west. " Boxing the 
compass" is to repeat all the points of the card; 
thus, commencing at north, we say, N. ; N. by 
E. ; N. N. E. ; N. E. by N. ; N. E. ; N. E. by E. ; 
E. N. E. ; E. by N. ; E. ; and so on round to 
north again. Beginners are made to " box the 
compass," to teach them the points and their 
names. 

The needle is attached to the under part of 
the card, with its north end directly under the 
north point of the card. In its centre is a socket, 
and it is placed on a pivot which projects from 
the bowl. The bowl is made of brass, or wood. 

1 Columbus crossed the ocean with barely any other instru- 
ment than a compass to guide him ; it would puzzle a navigator 
of the present day to do so without one. 



The Mariner s Compass. 205 

Now as the needle moves on the pivot it 
carries the card with it, and the north end 
points north. The bowl containing the card is 
placed in a stand, called the Binnacle, which is 
placed just in front of the helmsman. The 
bowl has a black vertical line drawn in it, and is 
placed so that this " mark " is in the vertical 
plane passing through the keel of the ship. It 
is called the " lubber's mark," and it indicates 
the direction of the ship's head. The bowl is 
suspended by gimbals, so that however much 
the ship may roll and pitch, the card is always 
horizontal. 

You see, then, the point of the compass card 
which is on the " lubber's mark " shows the 
direction of the ship's head; and the helmsman, 
after receiving the " course " to be steered, 
moves the helm until that point of the card is 
on the " lubber's mark." He keeps that mark 
on, until he receives orders to change the course. 

When Flavio Gioja made his first compass — 
as the kingdom of Naples at that time belonged 
to the Royal family of France — he marked the 
north point of the card with a fleur-de-lis — and 
the mark has been preserved. 

In the 15th century 1 the great maritime na- 
tions were Portugal and Spain — or at all events, 

1 The Encyclopaedia Britannica says: "John II., who as- 
cended the throne of Portugal in 1481, employed Roderick 



206 Familiar Talks on Astronomy, etc. 

they were the nations that were engaged in 
making new discoveries. The Portuguese con- 
fined themselves to endeavoring to reach the 
southern extremity of Africa. In 1487 Barthol- 
omew Diaz succeeded in reaching it; and in 
1497 Vasco de Gama doubled it, and arrived at 
Goa, on the west coast of Hindostan. It is 
worthy of note that Bartholomew Columbus, a 
brother of Christopher Columbus, accompanied 
Diaz on his voyage to the Cape. 

Leaving the Portuguese navigators, let us 
turn our attention to Christopher Columbus, the 
boldest navigator of his day; indeed, according 
to my view, the boldest man of whom we have 
any account in history. While all the other sea- 
men of the known world were creeping along 
the shore, he heroically sailed forth on the 
broad ocean. 

I will call to your attention three points. 
First, what astronomical knowledge did he 
possess? Secondly, what reasons had he for 
asserting he could reach China by sailing west- 
ward? Thirdly, what nautical instruments did 

and Joseph, his physicians, and Martin de Bohemia from Fayal, 
to act as a committee on navigation. They calculated tables 
of the sun's declination, and invented the astrolabe, — or at 
least recommended it as more convenient than the cross-staff. 
The navigator of that day had a compass, a cross-staff or as- 
trolabe, a moderately good table of the sun's declination, a cor- 
rection for the altitude of the pole star, and occasionally a very 
incorrect chart." 



Voyage of Columbus. 207 

he have to assist him in finding his position and 
shaping his course? 

(1). As Copernicus only published his work 
in 1543, Columbus, who sailed in 1492, did not 
know anything about the Copernican theory. 
He probably believed in the Ptolemean theory, 
and supposed the sun and other heavenly bodies 
to revolve about the earth. But he believed the 
earth to be round, and that he could reach the 
eastern confines of Asia by sailing westward. 
He did not know it, as we do, because no ship 
had ever sailed round it. He greatly under- 
estimated the dimensions of the earth; he sup- 
posed it much smaller than it really is. We 
have seen thai its exact measurement was not 
completed until the middle of the 18th century. 

He had no means by which to ascertain his 
longitude ; but he had an instrument, called the 
astrolabe, by which he could measure the al- 
titude of the sun and stars. If he was provided 
with an ephemeris, giving the sun's daily de- 
clination, he was able to find his latitude by that 
luminary. I think it more probable he found 
his latitude by observations of the pole-star. 
The altitude of the pole is the latitude of a 
place, and if there were a star exactly at the 
north pole of the heavens, its altitude would be 
the same as our latitude. Now the pole-star is 
not exactly at the north pole of the heavens, it 
is i° 1 8' removed from it. But it is easy to see 



208 Familiar Talks on Astronomy, etc, 

that when it is at its upper culmination, the lat- 
itude will be equal to its altitude minus i° 18'; 
at its lower culmination, the latitude is equal to 
its altitude phis i° i8' — and when the star is 
due east or west of the pole, its altitude will be 
equal to the latitude, since in this case it is just 
as high as the pole. 

I am the more inclined to think Columbus 
discovered his latitude by the pole-star from 
the fact that the oldest works on navigation I 
have read give the positions of the " dipper " 
when the pole-star is in any of the four posi- 
tions I have just mentioned. Thus, one position 
of the " dipper" indicated that the pole-star was 
at its upper culmination; another, that it was 
due east of the pole, and so on. The navigator 
knew from these positions what correction to 
apply to the observed altitude of the star. Of 
course this was before the publication of an 
ephemeris. 

(2). What reasons had he for expecting to 
find land to the westward? 

We know that Columbus had made a voyage 
to Iceland before 1492. Iceland was discovered 
by the Norwegians in 860, and in 960 a Nor- 
wegian colony was established on the east coast 
of Greenland. In IOOI America was discovered 
by an Icelandic voyager, somewhere about the 
latitude 41 ° or 42 ; and it was known and visited 
by the Northmen for some centuries after. The 



Voyage of Columbus. 209 

Northmen are supposed to have landed in the 
vicinity of Cape Cod. Why they should have 
described the climate as mild, and why they 
called the country Vinland, has always been a 
puzzle to me. The climate is not mild ; nor is 
there, in New England, a superabundance of 
grapes. 

Columbus may have learned at Iceland of the 
colony in Greenland, and the voyage of the 
Northmen. His profession of a seaman would 
naturally put him in the way of picking up in- 
formation of the kind ; and moreover, he was a 
" maker of maps." 

But Columbus, whatever he may have learned 
in Iceland, certainly sailed on his voyage with a 
definite object ; and that was to find land in about 
latitude 28 north. If he had simply intended 
to visit the land discovered by the Northmen, he 
would have sailed about west by north from 
Palos. What did he do? He went first to the 
Canary Islands, in latitude 28 N., and from 
thence sailed due west. Had he not been di- 
verted from his course by the opinions of the 
Pinzons, and the flight of birds to the southward 
which caused him to sail more in that direction, 
he would have struck the coast of Florida in the 
neighborhood of Cape Carnaveral. 

I confess I have never been able to discover 
why Columbus adhered so obstinately to his 
"due west " course from the island of Gomera. 
14 



210 Familiar Talks on Astronomy \ etc. 

Is it possible that he had some information un- 
known to the rest of the world ? 1 

(3). What nautical instruments did he have? 
The compass, and a rude instrument called an 
astrolabe, to observe altitudes. He could deter- 
mine his latitude, but his longitude he could 
only guess at. He measured time by an hour- 
glass. This glass was turned at the end of every 
hour; and it was in use for many years after 
Columbus's time. This is why we see in the 

1 This point has been much discussed. M. Marmontel in 
"The Incas, or the Destruction of the Empire of Peru," 
Dublin, 1777, says: — 

" In 1484 Alonzo Sanches de Huelua, going from the Cana- 
ries to Madeira, had been driven, it is said, almost to San 
Domingo. He returned to Tercera with only four of his com- 
panions. In this island Christopher Columbus, a famous pilot, 
by birth a Genoese, received them. They all died in his house, 
and it is reported that from their journal he undertook the 
discovery of America." 

And Fructuoso says that a Biscayan vessel arrived at Fun- 
chal, Madeira, in i486, and that the pilot gave Columbus, who 
sheltered him, the same information. 

All this appears sufficiently circumstantial, though neither 
Marmontel nor Fructuoso give their authority. 

Per contra : We know that Columbus went to Spain in 
1484, and that he had previously offered his services to 
Genoa and Portugal. Furthermore, we find him as early as 
1474 expounding his views to Paolo Toscanelli, the famous 
cosmographer. 

Nevertheless, all this does not explain why he sailed due 
west from Gomera ; for although, as early as 1474, he believed 
he could reach the Indies by sailing to the westward, he may 
have received information between that date and 1492 which 
induced him to pursue the course he did. Quien sabe ? 



Voyage of Columbus. 2 1 1 

old voyagers such expressions as, "we fought 
this tall ship for three glasses," meaning three 
hours. It was their only means of measuring 
intervals. Frequent references are made by the 
old poets to the use of the hour-glass. Thus, 
Shakspeare says, — 

" Or four and twenty times the pilot's glass, 
Hath told the thievish minutes how they pass." 

Columbus had no means for determining the 
speed of his ship, so far as I know. The first 
mention of the log and log-line is in Pigafetta's 
account of Magellan's voyage in 1519. 1 He 
must have estimated the number of miles run 
daily. 

Let us now glance at this voyage of Colum- 
bus, see what scientific discoveries he made, 
and what land of the western hemisphere he 
first saw. 

Sailing from Palos in Spain he touched at the 
Canary Islands, and then steered west across 
the Atlantic Ocean. He found, to his surprise, 
the wind blowing constantly from the northeast. 
This was a fair wind ; but the sailors, already 
sufficiently in dread of the voyage, complained 

1 This is from my recollectionof Pigafetta's narrative. The 
Encyclopaedia Britannica says, however : " There was not till 
1607 any means whatever of measuring a ship's progress 
through the water, and none in general use till 20 or 30 years 
later." 



212 Familiar Talks on Astronomy, etc. 

that they would never be able to get back to 
their native land. This wind, that blows almost 
constantly from the northeast in the north tropic 
zone, is known as the trade-wind; so called, 
because these winds facilitate trade. 

This will be a good time for me to explain 
the cause of these winds, as I promised in a 
former talk I would do. 

All winds are caused by the sun's heat, and 
the earth's rotation upon its axis. The trade 
winds blow between the parallels of about 25 
degrees north and south of the equator. They 
blow from the northeast in north latitude, and 
from the southeast in south latitude, and are 
caused by the air being heated in the equatorial 
regions. The hot air rises, thus creating a 
vacuum which the colder air from the north and 
south rushes in to occupy. If the earth did not 
revolve upon its axis these winds would be from 
the north and south ; but in consequence of its 
movement from west to east, and the fact that 
the diurnal velocity is greater at the equator 
than in the frigid and temperate zones, these 
winds appear to hang back, as it were, and thus 
blow from the northeast and southeast. . 

This apparent change in the wind's direction, 
in consequence of these two motions, is some- 
what like the cause of the aberration of light. 

The theory in regard to the movement of the 
heated air that rises at the equator is that it 



The Trade Winds. 213 

returns in the direction of the poles; and be- 
coming cold, it falls again to the earth, some- 
where about latitude 30°, and as its velocity to 
the east is now greater than the parallel of 30 , 
it becomes a southwest wind in the northern 
hemisphere, and a northwest wind in the south- 
ern one. 

A knowledge of the winds is essential to the 
seaman, especially in vessels propelled by sails 
alone. Speaking generally, we find, in the 
northern hemisphere, westerly winds between 
the parallels of 50 and 30 ; then a belt of 
calms (called the " horse latitudes " *) for a few 
degrees; then from about the parallel 25 ° to 
near the equator, northeast and easterly winds ; 
and then a belt of calms again for a few degrees 
on both sides of the equator. Proceeding south, 
we strike the southeast trades until we get to 
about 25 °, then a belt of calms, and after that 
northwest and westerly winds. The trade-winds 
are modified by the change in the sun's decli- 
nation, and near the land are changed into land 
and sea breezes. We have local winds, such as 
the sirocco, the harmattan, the monsoons, etc., 
all of which are treated of in our books on 
meteorology. 

1 This belt of calms received the name of " horse latitudes " 
from the New England traders, who formerly carried large 
numbers of horses to the West India islands, many of which 
were lost in these calms. 



214 Familiar Talks on Astronomy, etc. 

The first discovery made, then, by Columbus, 
was the trade winds. 

Proceeding on his voyage, he soon found a 
portion of the ocean which was covered with 
sea-weed ; and so thick was it that his vessels, 
being small, were impeded by it This weed 
bears globules, and Columbus's sailors thought 
they resembled a grape grown in Portugal, 
called the sargasso. This name was given to 
that portion of the ocean by Columbus. It is 
known as the Sargasso Sea, and the weed is 
found there now just as it was in 1492. 

The next discovery made by our voyagers 
was a more startling one, and that was that the 
north point of the needle did not point to the 
same star that it did in Spain. We are told the 
sailors were very much alarmed by this ; and 
well they might be, for if the compass failed 
them, all hope of finding their way back again 
was gone. 

This is known as the " variation of the com- 
pass." The needle does not point in the same 
direction at different places on the earth's sur- 
face. At some places it points due north; at 
others it points to the east of north; and at 
others again to the west of north. Moreover, it 
is constantly changing, though very, very slowly. 
We do not know the cause of this variation, 
any more than Columbus did ; but we can find 
its amount by observations of the heavenly 



Landfall of Columbus. 215 

bodies, and apply it to obtain the true north 
point. 

Columbus, then, had made three discoveries 
before he discovered land : The trade-winds, 
the Sargasso Sea, and the variation of the 
compass. 

What land did he first see? When Washing- 
ton Irving was writing the History of Columbus 
he engaged Captain Alexander Slidell Mac- 
kenzie, of the United States Navy, to investigate 
this point. After an exhaustive analysis, the 
captain came to the conclusion that the first 
land sighted by Columbus was the island in the 
Bahama group, called now Cat island. It was 
called by the natives Guanahani, and by the 
Spaniards San Salvador. 

The point has been disputed. The English 
say it was Watling's island ; the Spanish histori- 
an Navarrete thinks it was Turk's island; and 
books have been written to prove that it was 
Mariguana island, and Samana island or Atkins 
Key. 

The question must remain forever undecided. 
We know that Columbus, after leaving the first 
island, sailed along the coast of Cuba, and then 
along the coast of Hayti. On the north side of 
the latter island he built a fort, called La Navi- 
dad, left a garrison there, and returned to Spain. 
All we know about this place is that it was 



2i6 Familiar Talks on Astronomy, etc, 

probably near the present town of Cape 
Haytien. 

Upon the return voyage Columbus was forced 
by the easterly winds and Gulf Stream to sail to 
the northward until he got to the zone of the 
westerly winds ; so in addition to his other dis- 
coveries he may be said to have discovered the 
best route from Spain to the West Indies, and 
return. 

I have dwelt upon Columbus's voyage, his 
small astronomical knowledge, and his imperfect 
nautical instruments, because in my next talk I 
intend to tell you how a navigator of the present 
day is supplied; what correct charts, instru- 
ments, etc., he is furnished with, and how he 
finds his position at sea. 

When I look back upon my own voyages and 
recall the many anxious moments I have passed 
when looking for a port at night, and when I 
compare my own situation, supplied with accu- 
rate charts, perfect instruments, good sailing 
directions, everything in short that science can 
supply, and then think of Columbus in his little 
bark, his only instruments an imperfect compass 
and a rude astrolabe, sailing forth upon an un- 
known sea, I must award to him the credit of 
being the boldest seaman that ever " sailed the 
salt ocean." 



TALK THE FOURTEENTH. 

i 

The Sextant. Index Correction. Semi-Diameter. Dip 
of the Horizon. Refraction. Parallax. Departure. 
Course and Distance. Log-Book. Log and Line. 
Difference of Latitude and Difference of Longitude. 
Method of finding the Latitude by the Sun's Meridian 
Altitude. The Chronometer. Method of finding the 
Longitude by Chronometer. The Lunar Observation. 
Charts. Azimuth and Amplitude. Calculation of the 
Time of Sunrise and Sunset. The Artificial Horizon. 
Error and Rate of a Chronometer. Distance at which 
an Object is Visible at Sea. High Water. The Mer- 
chant Marine. 

LET us see what a navigator of the present 
day provides himself with before starting 
on a cruise. The astronomical instruments I 
have mentioned as being in use in all observa- 
tories, — the meridian circle, the equatorial, etc., 

— cannot be used on board ship. Why? The 
earth, as we have seen, is a movable observatory, 

— that is bad enough, — but a ship is a rolling 
and pitching observatory. Any of the instru- 
ments I have named would be thrown out of 
adjustment at the first swell of the ocean. 

Fortunately the seaman has been supplied 
with an instrument which overcomes this dim- 



218 Familiar Talks on Astronomy, etc. 

culty. It is called the sextant. It is held in 
the hand, and by a turn of the wrist the observer 
can keep the plane of the instrument in the plane 
of the two bodies whose angular distance he 
wishes to measure. It can be used to measure 
vertical angles, horizontal angles, or any other 
angles. In lunar observations the observer 
measures the angular distance between the 
moon and either the sun, a planet, or a lunar 
star ; 1 but the most common use of the sextant 
is to measure the altitudes of the heavenly bod- 
ies. By altitude is meant the angular height of 
a celestial body above the horizon. 

The navigator, then, supplies himself with a 
compass, sextant, an artificial horizon, 1 chro- 
nometer, log and log-line, hour-glasses, charts, 
box of instruments, barometer, thermometer, 
work on navigation, sailing directions, nautical 
almanac, and many other things not necessary 
to mention. It is my design to take you on a 
cruise with him, — say from New York to Rio 
de Janeiro, — and explain to you how he finds 
his daily position, and finally reaches his port. 

When the altitude of the sun is observed it 
has to be corrected for the index error of the 
sextant, for semi-diameter, dip, refraction, and 
parallax. I will take up these corrections seria- 
tim. The " index error " is the error of the 
sextant. All instruments have " errors." No 

1 See pages 237 and 243. 



Sem i- Diameter. 2 1 9 

instrument ever was, or can be, made perfect, 
and all observations whether made on shore or 
at sea have to be corrected for instrumental 
errors. 

The " index correction " 1 of the sextant is 
readily discovered by measuring the angular 
diameter of the sun ; it is plus or minus, as the 
case may be. 

Let us see what the correction for semi- 
diameter is. When we measure the altitude of 
the sun, what we want is the altitude of its cen- 
tre. Now there is no mark at the centre by 
which we can observe with the sextant when it 
is on the horizon ; so we bring the sun down to 
the horizon so that its lower limb (as we call it) 
is in contact with it, and then add the semi- 
diameter. This gives us the observed altitude 
of the sun's centre. 

Thus, in the diagram (Fig. 11) suppose A B 
to represent the line of the horizon ; S repre- 
sents the sun as it appears when " brought 
down " with the sextant ; and S' shows its posi- 
tion after the semi-diameter has been added. 

1 If a sextant is in perfect adjustment the true and reflected 
images of the sun, or other body, exactly coincide when the 
zero point of the index is on the zero mark of the graduated 
arc. But the horizon and index glasses may not be perpen- 
dicular to the plane of the instrument ; or they may not be par- 
allel when the index is on o ; or there may be some defect in 
the glasses. These errors make up what is called the " Index 
Correction." 



220 Familiar Talks on Astronomy, etc. 

The next correction is for " dip of the hori- 
zon." I have not had occasion to mention it 
before in the course of these talks, except that 





Fig. ii. 

I once said, " The higher you ascend the farther 
you can see." This is because the earth is 
round. 

In the diagram (Fig. 12) let O be the centre 
of the earth ; A an observer, elevated above its 
surface by the distance A B. The horizontal 
line A E represents the rational or true horizon, 
and the line A D, tangent to the earth's surface 
at C, the visible or sensible horizon. Now when 
we measure the altitude of S, the sun, we meas- 
ure the angle SAD; but the altitude we re- 
quire is the angle S A E ; hence we measure too 
much, by the angle E A D. Our horizon has 
" dipped " below the rational horizon by the 
angle E A D, and this angle is called the dip. 
We see, then, that the dip must be subtracted 
from the observed altitude ; and that its amount 
depends entirely upon the height of the ob- 
server. Tables are inserted in our books on 
navigation giving the dip corresponding to 
heights up to one hundred feet. The angle 



Dip of the Horizon. 



221 



E A D is small even up to one hundred feet, 
being for that height but 9/ 51". Navigators 
on the decks of their vessels are rarely over 
twenty-five feet above the level of the sea. 

I must call to your attention that the height 
A B, in the diagram, is very much exaggerated. 
All diagrams of the kind are. They are only 




Fig. 12. 

designed to illustrate. If I should attempt to 
draw it on a scale, the angle E A D, represent- 
ing the dip, even for one hundred feet, would 
be less than a pencil-mark. The distance O B 
being the radius of the earth, or four thousand 
miles, and the distance A B only fifty or one 
hundred feet. 

The correction for refraction is the most vex- 
ing of all the corrections, because it depends 



222 Familiar Talks on Astronomy •, etc. 

for its value upon the earth's atmosphere, which 
is constantly changing in density. When a ray 
of light passes obliquely from one medium to 
another of different density it is bent, or re- 
fracted, out of its course. This is best seen by 
placing a stick obliquely in water. Now the 
earth's atmosphere is not of uniform density; 
hence a ray of light from the sun, or other 
celestial body, upon entering it is bent more 
and more downwards, describing a curve, until 
it enters the eye of the observer. The observer 
sees the body in the direction of a line drawn 
tangent to the curve at the moment it enters 
the eye. He therefore sees it too high. In 
the diagram (Fig. 13) let O be the centre of 
the earth, and A an observer on its surface. 
Let B C represent the upper limit of the atmos- 
phere. Let S be any celestial body, and S D 
a ray of light from it which enters the earth's 
atmosphere at D ; it will then be refracted 
downwards, in a curve, until it reaches the eye 
of the observer at A; and he will see it in the 
direction of the line A S\ tangent to the curve 
at A, where it enters the eye of the observer. 
That is, he sees it too high ; hence the correc- 
tion for refraction must be subtracted from an 
observed altitude. Refraction, you observe, de- 
pends upon the altitude of a heavenly body; it 
is greatest when the object is in the horizon, 
and nothing when it is in the zenith. Tables of 



Refractio7i. 



223 



refraction are calculated for all altitudes, from 
o° to 90 , and inserted in works on navigation. 
It is a small quantity. The refraction for o°, 




Fig. 13. 

that is, when the body is on the horizon, is 
33'; and for 90 it is zero. 

As the apparent, 1 or angular diameter of the 
sun is about 33', the effect of refraction is to 

1 The apparent enlargement of the sun and moon in the hori- 
zon arises from an optical illusion. These bodies, in fact, are 
not seen under so great an angle when in the horizon as when 
on the meridian, for they are nearer to us in the latter case 
than in the former. The distance of the sun is, indeed, so great 
that it makes very little difference in his apparent diameter 
whether he is viewed in the horizon or on the meridian ; but 
with the moon the case is otherwise ; its angular diameter 
when measured with instruments is perceptibly larger at the 
time of its culmination. (Olmsted.) 

" Yet, like the sun, seems larger at his setting." 

(Robert Blair, 1700.) 



224 Familiar Talks on Astronomy, etc. 

elevate it by just its diameter when it is rising 
or setting; so that when we see the sun with 
its lower limb just touching the horizon, it is 
really just below it. Another effect is to make 
the day a little longer. 

The refraction is the same for all celestial 
bodies; it depends solely upon the altitude of 
the body. 

The last correction I have to explain is paral- 
lax. I have already told you what is meant by 
the horizontal parallax, and parallax in general. 

Observations of the celestial bodies compar- 
atively near the earth, when made at different 
places, do not give the same result, because 
they are viewed from different points. To 
correct this, astronomers have agreed to reduce 
them to what they would be if they had been 
made at the centre of the earth; and this cor- 
rection is called the parallax. It is the different 
direction in which a celestial body appears, as 
seen by an observer on the earth's surface and 
by one at its centre. 

In the diagram (Fig. 14) let O be the centre 
of the earth ; A an observer on its surface ; and 
S, S', two positions of a heavenly body. When 
the object is at S, that is, on the horizon, an 
observer at O would see it in the direction O S ; 
an observer at A, in the direction A S. The 
angle A S O is the horizontal parallax. It is 



Parallax. 



225 



the angle subtended at S by the earth's 
radius. 

When the object is at S', an observer at O 
would see it in the direction O S', and an ob- 



Fig. 14. 



server at A would see it in the direction A S'. 
The angle A S' O is the parallax in altitude. 

The correction for parallax is additive to an 
observed altitude ; for it is evident that we see 
the object too low. The parallax is greatest when 
the object is in the horizon; and it is nothing 
when the object is in the zenith. This is clearly 
15 



226 Familiar Talks on Astronomy, etc. 

seen by a reference to the diagram. The paral- 
lax, you observe, depends upon the distance of 
the body. It has nothing to do with its magni- 
tude. The moon has the greatest parallax, then 
the nearest planets, and then the sun. The stars 
(with the exceptions I have mentioned) have 
no parallax. Tables of Parallax are inserted in 
our books on navigation, calculated for all al- 
titudes, from o° to 90 ; and, as you see, there 
must be separate tables for the sun, moon, and 
planets. 

Let us suppose our navigator to sail from 
New York, bound to Rio de Janeiro. Just before 
he loses sight of the land he takes his " de- 
parture," as it is called ; that is, he observes the 
bearing of, say, Sandy Hook, and estimates its 
distance. The reverse bearing 1 is the first 
course entered on the log-book, and the distance 
is marked opposite to it. Every hour after this 
the log is thrown, and the course and distance 
run entered on the log-book. The theory of 
finding the speed of the ship by means of the 
log-line is this : Suppose we should throw over- 
board a log with a line attached to it, and then 
(supposing the log to remain stationary) we 
should let the line run out for the space of one 

1 By " reverse " bearing is meant the opposite bearing. 
Thus, if Sandy Hook bears west-northwest, distant 10 miles, 
the first course and distance is east-southeast 10 miles, starting 
from Sandy Hook. 



The Log and Line. 227 

hour, and then haul it in and measure it. 
Would not that tell us how many feet, or yards, 
or miles, the ship had sailed in an hour? Well, 
this is exactly the principle by which we deter- 
mine a ship's rate of sailing. We make it prac- 
tical, which this method certainly is not. A 
sea-mile is about 6,120 feet; and 51 feet is yj-g- 
of a mile, and 30 seconds is jJ-q of an hour. So 
if we put marks on the line at distances of 51 
feet apart and notice how many of these marks 
run out in 30 seconds, it tells us how many 
miles per hour the ship is sailing at the time the 
log is thrown ; and if we suppose the rate has 
been uniform for an hour, it shows how many 
miles the ship has made in that time, — for 30 
seconds is the same part of an hour that 5 1 feet 
is of a mile. 

The man, then, who heaves the log, knows 
the rate of sailing by the number of the knots in 
the mark he holds in his hand at the expiration 
of the 30 seconds ; and, no doubt, in this way a 
sea-mile came to be called a knot. 

Sand-glasses are used by seamen in heaving 
the log, as they are less liable to be broken than 
watches, and are more easily observed at night. 
I believe this is about the only use now made of 
sand-glasses, though formerly seamen used 
hour-glasses entirely for their time. For con- 
venience in separating the knots into eight 
fathoms of six feet each, navigators use 



228 Familiar Talks on Astronomy, etc. 

28-second glasses instead of 30-second glasses, 
but the principle is the same. 

The log-chip is a triangular piece of wood, 
one side of which is weighted with lead. It is 
attached to the end of the log-line by a cord 
from each of its three corners, forming what we 
call a bridle. When it is thrown into the water 
the lead causes it to assume an upright position; 
and it offers sufficient resistance to cause the 
log-line to run off the reel, and itself remains 
stationary. This is not absolutely true, but it is 
sufficient for our purpose. 

Well, then, the course and distance being 
entered on the log-book every hour, the next 
day, at noon, the navigator takes all the courses 
and distances, and by means of a " traverse 
table," inserted in his book on navigation, he 
finds his difference of latitude and difference of 
longitude made good, and applies it to the lati- 
tude and longitude of Sandy Hook. He thus 
finds his own latitude and longitude. This is 
what is called the " dead reckoning." It is in- 
dependent of celestial observations ; it depends 
upon the compass and log-line only. This 
reckoning is kept from day to day because it is 
what we depend upon when we can get no 
celestial observations, on account of fog, or 
cloudy weather. 

But the true position of the ship is found by 
observations of the sun, moon, planets, and 



Finding the Latitude. 229 

stars. The principle being the same for all, I 
will only speak of observations of the sun, — 
that being the body which we observe ninety- 
nine times in a hundred. I will first explain the 
theory of finding the latitude. It is very simple ; 
as is also that by which we find the longitude. 

The latitude of a place is its distance north or 
south of the equator. To find our latitude, 
then, we have to find the distance of our zenith 
from the equator. 

Now the navigator goes on deck with his sex- 
tant and observes the sun's meridian altitude. 
He does this by commencing his observations 
about ten minutes before noon, and noting the 
greatest altitude the sun attains. The sun is 
then on the meridian, and it is twelve o'clock 
apparent time. After the sun has crossed 
the meridian, it begins to fall; this is called 
" dipping." 

The sun's meridian altitude subtracted from 
90 , gives us the distance of the sun from the 
zenith — or its zenith distance. The Nautical 
Almanac contains the sun's declination, or its 
distance from the equator, north or south. 
Now then, as we know the distance of the sun 
from our zenith and the distance of the sun 
from the equator, we have only to combine the 
two to find the distance of our zenith from the 
equator, or our latitude. For example, sup- 
pose the sun's meridian altitude to be 6o°, bear- 



230 Familiar Talks on Astronomy, etc. 

ing south. Its zenith distance then is 30 . 
Suppose the sun's declination to be io° north. 
We have then for the distance of the zenith from 
the equator, or the latitude, 30 + io° = 40 N. 

If the observer happens to be in the Arctic 
regions during the summer months, the sun will 
always be above the horizon, and sometimes 
will be on the meridian twice 1 in the course of 
twenty-four hours, — once bearing south, and 
once bearing north. The latter is called its 
lower culmination. If we take its altitude at 
that moment, the latitude is found by adding it 
to the sun's polar distance (that is, 90 minus 
the sun's declination.) This gives us the dis- 
tance of the pole above the horizon, and this is 
equal to the latitude. 

At the equator the pole is on the horizon ; and 
for every degree we move north, the pole rises 
one degree above the horizon. Hence we have 
for another definition : the latitude of a place 
is equal to the altitude of the elevated pole. 

The theory by which we find the latitude, then, 
you observe, is very simple. We generally use 
the sun, but we use also the moon, planets, and 
stars. The " observed altitude," you must under- 
stand, is corrected for index-error, semi-diameter, 
dip, refraction, and parallax. The altitude of a 
star, however, requires no correction for semi- 
diameter and parallax, as it has none. 

1 It depends, of course, upon its declination. 



Finding the Latitude. 



231 



What I have said concerning the method of 
finding the latitude by the meridian altitude of a 
celestial body appears very clear from an in- 
spection of the following diagram. 




Fig. 15. 

Let the diagram be a projection of the celes- 
tial sphere on the plane of the meridian N. Z. S. 
Z is the zenith ; N S the horizon ; P the elevated 
pole ; P P' the axis of the sphere ; E Q the equa- 
tor ; Z Q the distance of the zenith from the 
equator, and P N the altitude of the pole. Z Q 
and P N are each equal to the latitude L. Let 
M, M 7 , M /f , be three positions of the sun on the 
meridian; Q M, Q M', and EM" represent its 
declination, d; and Z M, Z M', and Z M", repre- 
sent its zenith distance, z. 

When the sun is at M, north of the equator, 
L = z + d; when the sun is at M', south of the 



232 Familiar Talks on Astronomy, etc. 

equator, L = z — d\ and when it is at M", be- 
low the pole, L = altitude + /, the polar dis- 
tance, as I have said. 

I will now tell you how we find the longitude 
by chronometer. 1 A chronometer is a large 
watch of peculiar construction, made especially 
for the use of navigators. It is suspended by 
gimbals, as a compass-bowl is ; and the object 
is to keep the face of the chronometer hori- 
zontal. It is kept in a box in the navigator's 
cabin, and preserved as much as possible from 
changes of temperature and jars; for upon it 
depends our means of finding the longitude. 

The chronometer shows the mean Greenwich 
time. It is set at the observatory to that time, 
and then sent to the navigator. Now it does not 
really show the exact hour, minute, and second 
of Greenwich time. As I have said, a perfect 
instrument was never yet made, and never will 
be. But before leaving port the navigator 
knows the error and rate of his chronometer; 
that is, how much it is fast or slow of Green- 
wich mean time, and what it gains or loses 
daily. Knowing the error he applies it to the 
chronometer time, adding or subtracting as the 

1 The Encyclopaedia Britannica says : " Watches were un- 
known till 1530, and immediately Gemma Frizou, or Frisius, 
seized the idea for the purpose of ascertaining the difference 
of longitude between two places." 



Longitude by Chronometer. 233 

case may be, and finds the true Greenwich time. 
We see, then, the navigator has only to look 
at his chronometer to discover the mean Green- 
wich time. 

Now by observations of the heavenly bodies 
we can find our mean local time. Here, then, 
we have at once the theory of finding the 
longitude by chronometer. The difference be- 
tween our time and the time at Greenwich is 
our difference of longitude. There are fifteen 
degrees of longitude to one hour of time. We 
calculate our mean local time, the chronometer 
gives us the mean Greenwich time, the differ- 
ence between the two is our difference of longi- 
tude in time ; we multiply it by fifteen, and 
we find our longitude in degrees and minutes 
of space. 

Let us see how we compute our local time. 
I see in " Lockyer's Astronomy," page 100, 
American edition, the following: — 

" By this easy process navigators determine their 
longitude at sea. Taking with them a chronometer 
(an accurate watch) set according to the time of a 
given place (as Greenwich or Washington), they 
ascertain the local time by observing with the sextant 
when the sun is at its highest point ; it is then noon. 
Reducing the difference of time to difference of 
longitude they find that they are so many degrees 
east or west of the meridian of the place for which 
their chronometer is set." 



234 Familiar Talks on Astronomy, etc. 

All this is sufficiently absurd; but I do not 
hold Mr. Lockyer responsible for the statement, 
as I have seen it in some American astronomies. 
It agrees with what I have had occasion to 
observe concerning the so-called " navigation " 
taught in our colleges and schools. 

If we could note the exact moment the sun 
is on the meridian it would then be twelve 
o'clock, apparent local time; and by applying 
the equation of time to it we should have the 
mean local time; and the difference between 
it and the time shown by the chronometer at 
the moment of observation would be the differ- 
ence of longitude in time. But we cannot de- 
termine the instant of the sun's attaining its me- 
ridian altitude. It is true that in the tropics, 
where the sun has always a high meridian alti- 
tude, we can mark it pretty closely; but in 
other latitudes, especially when the sun's meri- 
dian altitude is low, we cannot mark it within 
three or four minutes, — and a minute of time 
represents fifteen miles of longitude ! Naviga- 
tors never rely upon this method to determine the 
longitude. 

The longitude by chronometer is found thus : 
In the morning or evening when the sun is 
fifteen or twenty degrees high, and is rising or 
falling rapidly, the navigator observes its alti- 
tude. He calls it a " time " sight ; because he 



Longitude by Chronometer. 2$$ 

is really going to compute his local time by 
means of the altitude he has just measured. 
At the instant of observing the altitude, he 
notes the time by his chronometer. 

He then solves a spherical triangle, of which 
he has given, the three sides, namely : the alti- 
tude just observed, the latitude, and the sun's 
polar distance. The latitude is really found at 
noon, as I have just explained, and is " worked 
back " to the time of taking the morning ob- 
servation. The polar distance of the sun is 
ninety degrees minus its declination, which 
declination is found in the Nautical Almanac. 

He solves the triangle, then, by means of 
its three sides and finds the angle at the pole. 
This angle is the sun's hour angle, or the ap- 
parent local time. To the apparent time he 
applies the equation of time (found also in the 
Nautical Almanac), and this gives him his mean 
local time. The difference between the mean 
local time and the Greenwich time (as indicated 
by the chronometer), is the difference of longi- 
tude in time. 

This is the simple theory of finding the longi- 
tude by chronometer. It is very easily com- 
prehended. Let the diagram (Fig. 16) repre- 
sent the projection of the celestial sphere on 
the plane of the horizon of a place, Z is the 
zenith, N Z S the meridian, P the elevated pole, 
M the position of the sun, or any other celestial 



236 Familiar Talks on Astronomy, etc. 

body. The navigator solves the triangle Z P M 
of which he knows P Z, the complement of the 
latitude; P M, the polar distance; and Z M, 
the zenith distance of the object, and he finds 
the angle Z P M, or the hour angle. 




The longitude by chronometer can be found 
by measuring the altitude of the sun, moon, 
planets, or stars ; the principle is the same for 
all. 



Before the introduction of chronometers the 
longitude was found by what is called the "lunar 
observation," first proposed by John Werner of 
Nuremburg, and improved upon by Maskeline. 1 

1 The Encyclopaedia Britannica says : — 
" Johann Tobias Mayer was born at Marbach, in Wiirtem- 
berg, Feb. 17, 1723. His great fame rests on his lunar tables, 



The Lunar Observation. 237 

The angular distances of the moon from the sun, 
from four planets (Venus, Jupiter, Mars, and 
Saturn), and from nine stars (called lunar stars 1 ), 
are given in the Nautical Almanac for the begin- 
ning of every third hour of mean time, for the 
meridian of Greenwich. The observer measures 
with a sextant the distance of the moon from 
one of these bodies, and after a long and intri- 
cate calculation (technically called " clearing 
the distance ") he deduces the Greenwich time 
at the moment of observation. The observation 
of the moon's altitude, taken when the " dis- 
tance " is measured, enables him to compute his 
own time ; the difference between the two times 
is the longitude in time, as before. 

You see what an amount of trouble is saved 
by having a chronometer. All the work in a 
" lunar" is in finding the Greenwich time corre- 
sponding to the " distance " we measure. We 
find the time between the three hours by pro- 
portional parts. When we have a chronometer 
we can note the Greenwich time at any instant. 

which were published in 1753. These tables, which were com- 
pared by Bradley with the Greenwich Observations and found 
to be sufficiently accurate to determine the longitude at sea to 
within half a degree, solved the problem of practically deter- 
mining longitude anywhere on the earth's surface." 

Maskelyne (1732-1811) was the Astronomer- Royal at Green- 
wich for nearly half a century. The British Nautical Almanac 
was established by him in 1766. 

1 These stars are ; Arietis, Aldebaran, Castor, Regulus, 
Spica, Antares, Formalhaut, Pegasi, and Aquilae or Altair. 



238 Familiar Talks on Astronomy, etc. 

Chambers's Encyclopaedia says : — 
" This use of chronometers was first distinctly pointed 
out by Sir Isaac Newton. A committee of the House 
of Commons, of whom this philosopher formed one, 
having been appointed on the nth June, 17 14, to con- 
sider the question of encouragement for the invention 
of means for finding the longitude, the result of their 
meetings was a memorial containing an explanation 
of the different means proper for ascertaining the lon- 
gitude, and recommending encouragement for the 
construction of chronometers as the best means of as- 
certaining it. An act of parliament was then passed, 
offering a reward for this purpose. 

'•'The first chronometer used at sea was invented 
by John Harrison. After many years of study it was 
completed in 1736. After several further trials and 
improvements, and two trial voyages to America, under- 
taken for the satisfaction of the commissioners, the 
last of which was completed on the 18th September, 
1764, the reward of ^20,000 was finally awarded to 
Harrison." 

The faith in chronometers 1 made its way slowly 
among seamen; even in the early part of the 

1 Even so late as 1844, Dr. Lardner said of chronometers : 

" Although the art of constructing time-keepers has been 
brought to a high degree of perfection by the skill of modern 
artisans, these instruments are even yet, and probably will ever 
continue to be, too imperfect to be implicitly relied upon. 

" In voyages or journeys which occupy months, we cannot 
rely on the indications of these instruments, even when most 
liberally provided or most perfectly constructed." 

This reminds one of Dr. Johnson's sagacious remark, that 
England would never become a commercial country. 



Charts. 239 

present century old navigators pinned their faith 
to the " lunar observation." They feared the 
chronometer would change its rate, or run down. 
Since about 1830, however, navigators have 
trusted to them implicitly. But as they are liable 
to accident, the Nautical Almanac continues to 
give the Greenwich time and lunar distances as 
before. Ships of war are usually provided with 
three chronometers ; merchantmen with but one. 

We see, then, our navigator on his voyage to 
Rio finds the position of his ship daily, and 
marks it upon his chart. After marking the 
chart, he shapes his course for the next twenty- 
four hours. The " chart" is provided by the 
Hydrographic Office, and is a delineation of the 
water and land between New York and Rio de 
Janeiro. As the seaman draws near his port, 
he consults a chart of the harbor to inform him- 
self more particularly of the marks and bearings 
by which to enter it. 

Should our navigator be in a sail-vessel, he 
stands from New York bound to Rio in a south- 
easterly direction, and may sight the Cape de 
Verde Islands. He soon gets the N. E. trades, 
and he then steers so as to cross the equator in 
about longitude 30 ; so that when he gets the 
S. E. trades he may be in a position to weather 
Cape St. Roque, the eastern extremity of South 
America. By sighting the Cape de Verde Is- 



240 Familiar Talks 07i Astronomy, etc. 

lands, or any other land whose position is well 
established, the navigator is enabled to " verify " 
his chronometer. 

The seaman watches the compass very closely. 
The variation of the compass differs in various 
latitudes and longitudes. It is easily found by 
celestial observations. By taking the altitude 




of the sun in the morning or evening we can 
calculate its true bearing ; and if we observe the 
compass bearing at the same instant, the differ- 
ence between them is the variation, provided 
there is no local attraction ; but in any case it 
is the " error " of the compass, whether made up 
of the " variation " and " local attraction " com- 
bined, or not. This is called finding the azi- 
muth of the sun, or its distance from the north 



Variation of the Compass. 241 

or south points. In the diagram (Fig. 16), page 
236, the azimuth is the angle PZ M. To find it 
we have given the three sides, just as we had in 
computing the sun's hour angle. 

Another method to determine the variation 
is to take the bearing of the sun at sunset or 
sunrise. We calculate its true bearing, and the 
difference is the variation. This is called finding 
the sun's amplitude, or distance from the east or 
west points. 

Let the diagram (Fig. 17) be a projection of 
the celestial sphere on the plane of the horizon ; 
N, S, the north and south points; E, W, the 
east and west points ; Z is the zenith ; P the 
elevated pole ; and let M be any celestial body 
on the horizon. Its amplitude is WM. 

The triangle P N M is right-angled at N. 
P N represents the latitude of the observer, and 
P M is the polar distance of the object. M N is 
equal to 90 minus the amplitude. To find it 
we have: 

cos. PM = cos. P N cos. M N, 
or, 

sine dec. 3= cos. lat. cos. M N ; 

hence, cos. M N, or the sine of the amplitude, 
is equal to sec. latitude into the sine of the 
declination. 

We see that the amplitude depends upon the 
declination of the object and the latitude of the 
observer. We can, then, assume all latitudes 
16 



242 Familiar Talks on Astrojiomy, etc. 

from o to 90 , and all declinations between o 
and 23^°, and calculate the sun's bearing. A 
table of this kind is inserted in our books on 
navigation. So that all the seaman has to do is 
to observe the bearing of the sun at sunset or 
sunrise by compass. The table gives him the 
true bearing. The difference is the error of his 
compass. 

The time of sunrise or sunset depends also 
upon the declination of the sun and the latitude 
of the observer. In the diagram (Fig. 17), the 
sun being on the horizon at M, the angle we 
wish to find is M P Z, or the sun's hour angle, 
or the apparent time of sunset. Since M P N 
is the supplement of M P Z, we readily see 
that, — 

cos. MPZ = — tang. dec. tang. lat. 

We calculate a table of this kind, also. It con- 
tains the time of sunrise and sunset for all lati- 
tudes and declinations. The seaman enters it 
with his latitude and the sun's declination, and 
finds at a glance the time of sunrise and sunset. 
It is the apparent time, of course ; but the 
navigator finds it convenient to keep apparent 
time when at sea; for, as he is continually 
changing his longitude, and consequently his 
time, he has to set his watch every day at 
noon. 



The Artificial Horizon. 243 

We have seen the use of most of the instru- 
ments I have mentioned as being essential to 
the seaman, viz., the compass, sextant, chro- 
nometer, log and line, etc. The artificial horizon 
is intended to use on shore when we cannot see 
the natural horizon. It is simply a shallow, 
rectangular box, or trough, filled with mercury. 
The observer stands at a little distance from it, 
where he can see the reflected image of the 
celestial object. He then, with the sextant, 
brings the body down until it just touches the 
reflected object; and since the angle of inci- 
dence is equal to the angle of reflection, he thus 
measures twice the altitude of the body. One 
half of this is the altitude, from which he com- 
putes his local time. The chronometer time 
being noted at the moment of observation, he 
can find its error. For in this case, as the 
longitude of the port is known, we add 1 the 
longitude in time to the mean local time, and 
this gives us the Greenwich time. The differ- 
ence between this true mean Greenwich time 
and the time shown by the chronometer is the 
error of the chronometer y fast or slow. 

After an interval of ten days the operation is 
repeated, and the error of the chronometer is 
again found. The difference between the two 
errors, divided by ten, gives the daily rate of the 
chivnometer, gaining or losing. It is hardly 

1 In east longitude we would subtract it. 



244 Familiar Talks on Astronomy, etc. 

necessary to say that a new error for the chro- 
nometer is found by the navigator at every 
port, and perhaps a new rate; but, as I have 
remarked, it does not matter how much it is, 
so long as we k7iow it. The test of a good in- 
strument is in the uniformity of its rate. 

We often hear it asked how far a ship can be 
seen at sea. In this case it is the sphericity of 
the earth, alone, that limits vision. The higher 
the observer, the farther he can see. A very 
simple problem in practical astronomy enables 
us to calculate the distance corresponding to 
different heights, and tables are calculated and 
inserted in our books. Thus, a mountain 1,000 
feet high can be seen 42 miles, a mountain one 
mile high can be seen 96 miles, and so on. 
Knowing the height of a mountain, we enter the 
table and find how far it can be seen ; and 
vice versa. 

An observer on the deck of a vessel, 20 feet 
above the sea, can perceive an object on the 
horizon six miles off; this is, in fact, the limit of 
his sensible horizon. If he were a hundred feet 
high, he would see 13 miles. If a sailor, then, 
20 feet above the water, sees on the horizon 
the royals of a ship which are 100 feet above 
the sea, the distance is 6 + 13, or 19 miles. 

One other point, and I have done. The navi- 
gator can calculate the time of high water at the 



N antic al Schools. 245 

port he is about to enter. At some places this 
is a matter of importance, — at Eastport, Maine, 
for example, where the tide rises and falls about 
20 feet. A vessel anchoring there in 18 feet of 
water at high tide, would find herself high and 
dry at low water. The time of high water at 
any port is readily found when we know the age 
of the moon and the time of high water on full 
and change days at that port, or the " establish- 
ment" of the port, as it is called. 

I hope I have given you at least an idea of 
the manner in which a seaman finds his way 
across the ocean. If you have followed me, 
you see that the theory of navigation is not 
difficult to understand. The art requires ex- 
perience. But just as there are good lawyers 
and bad lawyers, good doctors and bad doctors, 
so are there good and bad navigators. And I 
will close these talks with the remark that, 
although we have special schools for the lawyer, 
the doctor, the merchant, the farmer, the army 
officer, and the navy officer, many of which are 
largely endowed by the general Government 
and the States, we have no such schools for the 
merchant seaman. The State of New York 
keeps up the training-ship St. Mary's, and the 
Government keeps several training-ships ; but 
these are for apprentice boys for the navy only. 
So far as I know, it is only at a few private 



246 Familiar Talks on Astronomy, etc. 

schools in the large sea-ports that a MATE can 
learn anything of the art of navigation. 

The merchant-officer is intrusted not only 
with the property, but the lives of thousands of 
human beings ; and yet there is absolutely no 
college in this country where he can learn both 
the theory and practice of navigation. Mirabile 
dictu ! 



APPENDIX. 



DEFINITIONS. 

Aberration. A small apparent motion of the fixed stars 
occasioned by the progressive motion of light and the 
earth's annual motion in its orbit. 

Aerolites. An aerolite is a meteorite composed of stone. 

Aerosiderites. An aerosiderite is a meteorite composed 
of iron. 

Almanac. The Nautical Almanac is an almanac contain- 
ing the positions of the sun, moon, planets, and stars, 
and is prepared especially for the use of seamen. 

Altazimuth. An instrument for measuring altitudes and 
azimuths, as its name denotes. 

Altitude. The angular height of a celestial body above 
the horizon. On land it is measured by altazimuths, 
meridian circles, and other instruments. At sea it is 
measured by the quadrant or sextant. 

Amplitude. The angular distance of a heavenly body 
from the east or west points, measured on the 
horizon. 

Angle. An angle is the amount of divergence of two 
right or curved lines. 

Annular. Having the form of a ring. Applied to eclipses 
of the sun. 

Anomalistic. The anomalistic month is the time in 
which the moon goes from apogee to apogee again, 
or from perigee to perigee again. The anomalistic 



248 Appendix. 

year is the interval between the earth's passage from 
aphelion to aphelion again, or from perihelion to 
perihelion again. 

Anti-trades. This name is sometimes given to the south- 
west winds we find north of the Tropic of Cancer, 
and the northwest winds south of the Tropic of Cap- 
ricorn, between the parallels of 30 and 45 or 50 . 

Aphelion. The point in an orbit farthest from the sun. 

Apogee. The point in the moon's orbit farthest from 
the earth. 

Apsis, plural Apsides. The line of apsides is the line 
joining the aphelion and perihelion points. It is the 
major axis of elliptical orbits. 

Arc, Diurnal. The path described by a heavenly body 
between rising and setting. 

Aries, First point of. One of the points of intersection 
of the celestial equator and the ecliptic. Right as- 
cension and celestial longitude are reckoned from this 
point. 

Ascending Node. The point where the moon passes 
north of the ecliptic. 

Ascension, Right. The angular distance of a heavenly 
body from the first point of Aries (or the vernal 
equinox), measured on the celestial equator towards 
the east. It is reckoned in hours from o to 24. 

Asteroids. The small planets, over 280 in number, be- 
tween Mars and Jupiter. 

Astrolabe. A rude instrument used by the navigators 
of the 15th, 16th, and 17th centuries to measure the 
altitudes of the heavenly bodies. 

Astronomy. The law of the stars. 

Axis. The line on which a body rotates. 

Azimuth. The angular distance of a celestial body from 
the north or south points, measured on the horizon. 

Base-Line. A measured distance on which to found a 
system of triangulation. 



Appendix. 249 

Bode's Law. Explained in the text. 
Calendar. A method of reckoning time. 
Catalogue-Star. A list of stars giving their names, mag- 
nitudes, right ascensions, and declinations. 
Celestial. Appertaining to the heavens. Thus, we have 

the terrestrial meridian and the celestial meridian ; 

the terrestrial equator and the celestial equator ; the 

terrestrial poles and the celestial poles ; the one 

being the prolongation of the other to the heavenly 

sphere. 
Centrifugal Force. The force which gives a body mov- 
ing round another body a tendency to move off at a 

tangent to the periphery of the curve. 
Centripetal Force. The force holding a body towards 

the centre ; such as the attraction of the sun. 
Circumpolar. Round or near the pole. Applied to the 

stars which do not set. 
Clepsydra. A water-clock. 
Co-latitude. The latitude of a place subtracted from 90 . 

The complement of the latitude. 
Colures. The celestial meridians passing through the 

equinoxes and solstitial points, called the equinoctial 

and solstitial colures. 
Complement. What an arc or angle wants of 90 . 
Conjunction. Seen in the same direction. Celestial 

bodies are in conjunction when they have the same 

longitude. 
Constellation. A group of stars supposed to represent 

some figure. 
Culmination. The passage of a heavenly body across 

the meridian of the observer. A transit. 
Cycle. A period of time, such as a lunar cycle ; the 

cycle of eclipses, called by the Chaldeans Saros. 
Day. When we speak of a day in astronomy, we mean 

a solar day of twenty-four hours, unless we specify a 

lunar day or a sidereal day. 



250 Appendix. 

Declination. The angular distance of a heavenly body 
north or south of the celestial equator. The comple- 
ment of the declination is the polar distance. 

Degree. The 360th part of a circle, marked thus, °. 

Density. Compactness ; comparative weight. 

Descending Node. The point where the moon passes 
south of the ecliptic. 

Diameter. A right line, which, passing through the 
centre of a circle or sphere, divides it into two equal 
parts. 

Digit. In astronomy, the twelfth part of the diameter of 
the sun or moon, used in measuring the extent of a 
partial eclipse. 

Dip. The dip of the horizon is the depression of the 
sensible horizon below the celestial or true horizon. 

Disk. The visible surface of the sun, moon, or planets. 

Eccentricity. The eccentricity of an ellipse is the dis- 
tance of either focus from the centre, divided by half 
the major axis. 

Eclipse. Literally, a disappearance; caused by a body 
entering into the shadow of another. 

Ecliptic. The great circle (or more probably ellipse) of 
the heavens along which the sun appears to perform 
his annual journey ; the real path of the earth about 
the sun. 

Elements. Chemical elements refer to the substances 
found in the sun and stars, etc. The elements of the 
orbits of the planets are the distances from the sun, 
times of rotation, diameters, masses, etc. Elements 
of position are, right ascension and declination, lati- 
tude and longitude, altitude and azimuth, etc. 

Ellipse. An oval figure, an oblique section of a cone. 

Elongation. The angular distance of a planet from the 
sun. 

Ephemeris. An account of the daily motions and posi- 
tions of the celestial bodies ; an almanac. 



Appendix. 251 

Equator. The terrestrial equator is an imaginary circle, 
running round the earth half-way between the poles. 
It is called the equator because when the sun is on it 
the days and nights are of equal length. It is also 
called the equinoctial line. The plane of the equator 
produced to the heavens marks the celestial equator, 
or equinoctial. 

Equinoxes. The points of intersection of the ecliptic 
and the equator are called the vernal and autumnal 
equinoxes. 

Establishment. The interval at new or full moon be- 
tween the time of the moon's meridian passage 
and high water is called the " establishment of the 
port." 

Evening Star. Venus, when visible in the evening after 
sunset, is called the evening star. The ancients 
called it Hesperus, or Vesper. 

Faculae. The brightest parts of the solar photosphere 
are called faculae. 

Focus. The point of convergence, where the rays of 
light are concentrated by a lens or burning-glass ; 
plural, foci. 

Galaxy. The Greek name for the Milky Way, or Via 
Lactea. 

Geocentric. Viewed from the centre of the earth. 

Gibbous. Applied to the appearance of the moon be- 
tween its first quarter and full moon, and between 
full moon and third, or last quarter. 

Gnomon. The hand of a dial ; also in ancient times an 
instrument for measuring altitudes ; used by the 
Greeks for determining the sun's altitude as far 
back as 276 b. c. 

Gravity. Tendency to the centre ; weight. The specific 
gravity is the weight of the matter of any body, com- 
pared with the weight of an equal bulk of pure water, 
taken as a standard. 



252 Appendix. 

Great Bear. The constellation Ursa Major, called also, 
the " Dipper," " Charles 1 Wain," the " Seven Stars," 
the " Wagon." 

Harvest Moon. The moon in harvest-time (in England), 
near the autumnal equinox, when it rises near the 
same hour for several successive evenings. This 
occurs, usually, at the times of two full moons, one 
in September and the other in October. The first is 
called the harvest moon, the second the hunter's 
moon. 

Heliocentric. Viewed from the centre of the sun ; as 
opposed to geocentric. 

Hemisphere. If a plane be passed through the centre 
of the earth, at right angles to its axis, it divides the 
earth into the north and south hemispheres. A half 
sphere. 

Horizon. The line where the heavens and earth seem to 
meet is called the visible or sensible horizon. The 
rational or true horizon is a great circle of the 
heavens, the plane of which is parallel to the plane 
of the visible horizon, but which, instead of being a 
tangent to the earth's surface, passes through its 
centre. 

Horizontal Parallax. Explained in text. 

Hour-angle. The angular distance of a heavenly body 
from the meridian. 

Hour-circle. The circle attached to the equatorial in- 
strument, by which right ascensions are indicated. 

Hyperbola. One of the conic sections. 

Inclination. The inclination of an orbit is the angle 
between the plane of the orbit and the plane of 
the ecliptic. We have also the " inclination " of the 
earth's axis, the planets' axes, etc. 

Inferior Conjunction. When an inferior planet is in a 
line between the earth and sun, it is said to be in 
i7iferior conjunction with the sun. 



Appendix. 253 

Inferior Planets. The planets Mercury and Venus are 
called inferior planets, because their orbits are 
withift the orbit of the earth. 

Irradiation. A bright object makes a stronger impres- 
sion on the eye than a dim one, and appears larger 
the brighter it is, — this is called irradiation. 

Julian Calendar. The calendar as corrected by Julius 
Caesar. 

Latitude. Terrestrial latitude is the angular distance 
of a place, north or south of the equator. It is 
measured on a meridian. Celestial latitude is the 
angular distance of a heavenly body from the plane 
of the ecliptic. 

Limb. The edge of the disk of the sun, moon, or planet. 

Longitude. Terrestrial longitude is the angular dis- 
tance of a place, east or west of the meridian of 
Greenwich. It is measured on the equator. Celestial 
longitude is the angular distance of a heavenly body 
from the first point of Aries. It is measured on the 
ecliptic, and is reckoned up to 360 . 

Lunation. The period of the moon's journey round the 
earth. 

Mass. The quantity of matter a body contains. 

Meridian. The great circle of the heavens passing 
through the zenith of any place and the poles of the 
celestial sphere. 

Micrometer. An instrument for measuring small angu- 
lar distances. 

Nadir. The point beneath the feet. 

Neap. Twice in every lunar month the tides are lower 
than usual, this occurs about a day or two after the 
moon is in her quadratures. These are called neap 
tides. 

Nebula. A name given to faint, misty appearances, 
which are dimly seen among the stars, resembling 
a comet. 



254 Appendix, 

Nodes. The points at which a comet's or planet's 
orbit intersects the plane of the ecliptic ; one is 
termed the ascending, the other the descending node. 

Nutation. An oscillatory movement of the earth's axis 
due to the moon's attraction on the equatorial 
protuberance. 

Oblate. An oblate spheroid is a solid generated by the 
revolution of an ellipse about its minor axis. The 
equatorial diameter is, then, greater than the polar 
diameter. 

Obliquity (The) of the ecliptic is the angle the plane of 
the ecliptic makes with the plane of the celestial 
equator. 

Occultation. The eclipsing of a star or planet by the 
moon or a planet. 

Opposition. A superior planet is in opposition when 
the sun, earth, and the planet are in the same 
straight line, with the earth in the middle. 

Orbit. The path of a planet or comet round the sun, or 
of a satellite round a primary. 

Parallax. The difference between the true and the 
apparent direction of a celestial body, owing to a 
change in the place of the observer. 

Parallels. Imaginary small circles on the earth's sur- 
face, parallel to the equator, are called parallels of 
latitude. 

Penumbra. The half-shadow which surrounds the 
deeper shadow in an eclipse. 

Perigee. The point in the moon's orbit nearest the 
earth. 

Perihelion. The point in an orbit nearest the sun. 

Period. The period, or periodic time, of a heavenly 
body is the exact time it takes to complete one re- 
volution about the sun. A synodic periodic the time 
in which a planet returns to the same position with 
regard to the sun and earth. 



Appendix. 255 

Perturbations. The effects of the attractions of the 
planets and satellites upon each other, consisting of 
variations in their motions and orbits. 

Phases. The various appearances presented by the 
illuminated portions of the moon and inferior planets 
in different parts of their orbits. 

Photosphere. The exterior surface presented by a star, 
or the sun. 

Plane. A plane is a surface with which a straight line 
that joins any two of its points will coincide al- 
together. 

Polar. The line through the earth's centre from pole to 
pole, is called the Polar Diameter. Polar distance 
is the angular distance of a celestial body from the 
celestial poles. It is the co7?iplement of the declina- 
tion, or 90 minus the declination. 

Polaris. The pole-star, called also the north-star. 

Poles. The extremities of the imaginary axis on which a 
celestial body rotates. The poles of the heavens are 
the extremities of the axis of the celestial sphere. 

Precession. The precession of the equinoxes is a slow 
but continual shifting of the equinoctial points from 
east to west. The amount of precession annually 
is 50^ seconds ; hence it appears that the equinoc- 
tial points will make an entire revolution in 25,868 
years. 
-The Prime Vertical, The prime vertical circle is a 
great circle of the celestial sphere passing through 
the east and west points, and through the zenith, of 
course. 

Quadrant. An instrument used by seamen to measure 
the altitudes of the heavenly bodies ; but sextants 
are now almost universally used. 

Quadrature. Two heavenly bodies are said to be in 
quadrature when there is a difference of longitude of 
90 between them. 



256 Appendix. 

Refraction. In astronomy, deviation of a ray of light, 
owing to its passing through the earth's atmos- 
phere. 

Rotation. The motion of a body round a central axis. 
Thus the daily turning of the earth on its axis is a 
rotation; its annual motion round the sun is a 
revolution. 

Saros. A term applied by the Chaldeans to the cycle of 
eclipses. 

Satellites. The smaller bodies revolving about planets. 

Scintillation. The " twinkling " of the stars. 

Selenography. A description of the moon. 

Sextant. An instrument used by seamen for measuring 
the altitudes of, and angular distances between, the 
heavenly bodies ; also used in hydrographic sur- 
veying. 

Shooting-Stars. A name applied to meteors. 

Sidereal. Relating to the stars. 

Signs of the Zodiac. The celestial equator is divided 
into 12 signs of 30 each, and thus called. 

Solstices. The points in the sun's path at which the 
extreme north and south declinations are reached, 
and at which the motion is apparently arrested be- 
fore its direction is changed. June 21 is called the 
summer solstice, and December 21 the winter 
solstice. 

Spectroscope. An instrument used for the examination 
of the spectra of the heavenly bodies. 

Spectrum. The luminous colored band produced by the 
dispersion of light. 

Spring. The spring tides are the two highest tides that 
occur in a lunar month, a day or two after new and 
full moon. 

Superior Conjunction. When an inferior planet is in a 
line with the sun, but beyond it, it is said to be in 
superior conjunction. 



Appendix. 257 

Synodic Period. In consequence of the earth's motion, 
the period in which a planet regains the same posi- 
tion with regard to the earth and sun is different 
from the actual period of the planet's revolution 
round the sun. The time in which a position, such 
as conjunction or opposition, is regained, is called a 
synodic period. Thus, a lunar month is a synodic 
period. 

Syzygies. The two points in the moon's orbit corre- 
sponding to new and full moon. 

Termination. The boundary between the bright and 
shaded portions of the moon is thus called. 

Transit. The passage of a heavenly body across the 
meridian of a place. A culmination. Also, the 
passage of a heavenly body across the disk of an- 
other; such.ias a transit of Venus. 

Tropics. The circles of declination (of the celestial 
sphere) which mark the most northerly and southerly 
points in the ecliptic, in which the sun occupies the 
signs, Cancer and Capricorn, respectively. On the 
earth, a name given to two parallels of latitude, one 
(the tropic of Cancer) being 23 28' north of the 
equator, and ; the other (the tropic of Capricorn) 
being 23 28' south of the equator. 

Umbra. The darkest central portion of the shadow cast 
by a heavenly body in an eclipse. 

Universe. The whole creation, including the solar sys- 
tem, and all the starry regions beyond. 

Vertical. Placed or being in the zenith, or perpendicu- 
larly overhead. A vertical circle is one that passes 
through the zenith and nadir of the celestial sphere; 
it is perpendicular, of course, to the horizon. Alti- 
tudes are measured on vertical circles. 

Via Lactea. The Milky Way. 

Volume. The cubical contents of a body. 

Zenith. The point of the celestial sphere overhead. 
17 



258 Appendix. 

Zodiac. A portion of the heavens extending 9 on 
either side of the ecliptic, in which the sun and 
major planets appear to perform their annual revo- 
lutions. 

Zodiacal Light. A faint light, somewhat like the Milky 
Way, seen in the west shortly after sunset in winter 
and spring. Its origin is unknown, though there are 
many speculations concerning it. 

Zone. One of the five divisions of the earth's surface 
formed by means of the two tropics, and the two 
polar circles. 



INDEX. 



Aberration of light, 140. 
Absolute time, 181. 
Almagest, 27. 
Almanac, nautical, 239. 
Alpha Centauri, parallax of, 

154; 

Altazimuth, 201. 

Altitude, 218. 

Amplitude, 241. 

Angular diameter of sun, 44. 

Annular eclipse of sun, 107. 

Antarctic Circle, 40. 

Aphelion, 169. 

Apogee, 77. 

Apparent motion of sun, 42. 

Apparent solar day, 170. 

Apparent time, 170. 

Apsides, 180. 

Arctic Circle, 40. 

Argelander, 151. 

Aristarchus, 27, 39. 

Artificial horizon, 243. 

Asteroids, 137. 

Asteroids, force of gravity on, 

138- 
Astrolabe, 207. 
Astronomical day, 172. 
Astronomers, first, or early, 21. 
Astronomy defined, 17. 
Astronomy, nautical, 198. 



Autumn, length of, 48. 
Azimuth, 240. 

Bessel, 153. 
Bishop Wilkins, 116. 
Bode's Law, 132. 
Bradley, discoverer of aberra- 
tion of light, 141. 

Caesar, Julius, 24. 

Calendar, 24. 

Calendar, Gregorian, 26. 

Calendar, Julian, 25. 

Carlyle, 16. 

Cassini, 36. 

Cavendish experiment, 144. 

Chaldeans, 26. 

Charles's Wain, 165. 

Chart, 239. 

Chronometer, 232. 

Chronometers, introduction of, 
236. 

Chronometer, verifying, 240. 

Civil day, 172. 

Clepsydrae, 174. 

Climate of southern hemi- 
sphere, 45. 

Clocks, 176. 

Columbus, 29. 

Columbus, voyage of, 206. 



260 



Index. 



Comets, 161, 163. 
Compass, error of, 240. 
Compass, mariner's, 204. 
Compass, variation of, 214. 
Condamine, 36. 
Constellations, 155. 
Constellations, zodiacal, 158. 
Copernicus, 28, 207. 
Crepusculum, 53. 
Cycle, lunar, 89. 
Cycle, metonic, 89. 
Cycle of eclipses, no. 

Day, 23. 

Day, apparent, 170. 

Day, mean, 170. 

Day, sidereal, 170, 173. 

Days, long and short, 49. 

Days of week, 177. 

Day, universal, 188. 

Dead reckoning, 228. 

Density of earth, calculation 

of, 143. 
Densities of sun and planets, 

147. 
Departure, 226. 
Difference of latitude, 228. 
Difference of longitude, 228. 
Dip of the horizon, 220. 
Dipper, 156, 165. 
Distance of an object at sea, 

244. 
Dropping a day, 192. 

Earth, 30. 
Earth, axis of, 40. 
Earth, density of, 1 43. 
Earth's density calculated, 143. 
Earth's meridian measured, 34. 
Earth-shine, 76. 
Eclipse, moon, 108. 
Eclipse, sun, 106. 



Eclipses, 105. 

Eclipses, number of in any one 
year, 109. 

Ecliptic, 40. 

Ecliptic, obliquity of, 39. 

Egyptians, 26. 

Elements in sun and stars, 101. 

Ephemeris, nautical, 201. 

Equation of time, 171. 

Equator, an observer at, 62. 

Equatorial instrument, 201. 

Equinoxes, 41. 

Equinoxes, precession of, 159, 
166. 

Eratosthenes, 32. 

Error and rate of the chro- 
nometer, 243. 

Establishment of the port, 245. 

First meridian, 187. 
Flavio Gioja, 204. 
Foucault's experiment, 30. 

Galaxy, 160. 

Galileo, 28. 

Geography of the heavens, 157. 

Gioja, Flavio, 204. 

Glasses, hour, 210. 

Globes, use of, 157. 

Gnomon, 33. 

Golden number, 89. 

Greenwich meridian, 189. 

Gregorian calendar, 26. 

Heat of sun, no. 

Heat received from moon, 84. 

High water, 90. 

High water, head of, 91. 

High water, time of, 245. 

Hipparchus, 27. 

Hour-glass, 210. 

Hour, universal, 188. 



Index, 



261 



Horizon, 252. 
Horizon, artificial, 243. 
Horse latitudes, 213. 
Hutton, 146. 

Inclination of moon's orbit, 85. 
Index correction, 219. 
Initial point of day, 182. 
International conference, 187. 
Introduction of chronometers, 
238. 

Julian calendar, 25. 
Jupiter, description of, 129. 
Jupiter, satellites of, 105, 133. 
Jupiter, seasons of, 139. 

Kepler, 28. 
Kepler's laws, 141. 

Landfall of Columbus, 215. 

Latitude, 228. 

Librations, 77. 

Light, aberration of, 140. 

Light shed by moon, 84. 

Light, velocity of, 134. 

Local time, 181. 

Lode star, 203. 

Lodestone, 202. 

Log and line, 211, 226. 

Longitude and time, 181. 

Longitude by chronometer, 
233. 

Longitude by lunar observa- 
tion, 236. 

Lunar cycle, 89. 

Lunar day, 172. 

Lunar eclipse, 108. 

Lunar stars, 237. 

Magellan, 161, 195. 
Magellanic clouds, 161. 



Magnetic needle, 203. 
Marco Polo, 203. 
Mariner's compass, 204. 
Mars, calculation of distance 

of, 97. 
Mars, description of, 127. 
Mars, discovery of satellites of, 

"5- 

Maskelyne, 144. 
Mason and Dixon's line, yj' 
Mean day, 170. 
Mean time, 170. 
Mercury, climate of, 139. 
Mercury, description of, 118. 
Meridian circle, 200. 
Meridian, earth's measurement 

of, 34- 
Meridian, first, 188. 
Meridian, Greenwich, 189. 
Meridian, neutral, 191. 
Meridian, 180th, 195. 
Meridian, prime, 187. 
Meteors, 161. 
Meteorites, 162. 
Midnight sun, 54. 
Milky way, 160. 
Moon, attraction of gravitation 

at surface, 92. 
Moon, light shed by, 84. 
Moon, phases of, 66. 
Moon, rule for finding age of, 

72. 
Moon, the, 6^. 

Moon's angular diameter, 78. 
Moon's diameter, calculation 

of, 83. 
Moon's distance from the earth 

calculated, 78. 
Moon's heat, 84. 
Moon's horizontal parallax, 79. 
Moon's influence, 90. 
Moon's nodes, 85. 



262 



Index. 



Moon's orbit, inclination of, 85. 
Moon's revolution upon its 

axis, 77. 
Moon's rising, errors about, 73. 
Moon's surface, 85. 
Moon's volume, calculation of, 

S3- 

Month, 24, 178. 
Month, anomalistic, 178. 
Month, calendar, 178. 
Month, lunar, 76, 178. 
Month, nodical, 178. 
Month, sidereal, 76, 178. 
Month, synodic, 76. 
Month, tropical, 178. 

Nautical Almanac, 202, 239. 

Nautical astronomy, 198. 

Nebula, 160. 

Nebular hypothesis, 160. 

Needle, magnetic, 203. 

Neptune, description of, 131. 

Neptune, discovery of, 114. 

Neutral meridian, 191. 

Newton, Isaac, 28. 

Nodes, 85. 

North pole, an observer at, 59. 

North star, 156. 

Nutation, 167. 

Obliquity of the ecliptic, 40. 
Observers, early, 21. 
Occupations, 105. 
Occultations of Jupiter's satel- 
lites, 106, 133. 
Octants, 68. 

Parallax, 218, 224. 
Partial eclipse of sun, 107. 
Perigee, 77. 
Perihelion, 169. 
Phases of moon, 66. 
Photosphere, sun's, 101. 



Picart, 36. 

Planets, 112. 

Planets, density of, 146. 

Planets, inhabited, 138. 

Planets known to the ancients, 

US- 
Planets, masses of, 142. 
Planets, satellites of, 114. 
Pleiades, 165. 
Pope Gregory XIII., 25. 
Precession of the equinoxes, 

159- 
Prime meridian, 187. 
Ptolemy, 27. 
Pythagoras, 27. 

Quadratures, 68, 

Radius, vector, 141, 
Refraction, 218, 221. 
Relative time, 181. 
Repeating a day, 193. 
Reverse bearing, 226. 
Roemer, 134. 
Roger Bacon, 203. 
Rousseau, 17. 

Royal Society of England, 116. 
Rule for finding moon's age, 72, 
Running time, 185. 

Sargasso Sea, 214. 
Saros, no. 

Saturn, description of, 130. 
Schehallien, 145. 
Seasons, change of, 39. 
Secondary light, 76. 
Semi-diameter, 218. 
Seven stars, 165. 
Sextant, 218. 
Shooting stars, 161. 
Sidereal day, 170, 173. 
Sidereal time, 173. 



Index. 



2^3 



Solar eclipse, 106. 

Solar system, 113. 

Solstices, 40. 

Sound, rate of travel, 135. 

Southern hemisphere, climate 

of, 44. 
Specific gravity of the earth, 

143- 

Spectroscope, 101. 

Spectrum analysis, 101. 

Spring, length of, 48. 

Standard time, 183-185. 

Star-clusters, 160. 

Star-showers, 161. 

Stars, 149. 

Stars, circumpolar, 174. 

Stars, classification of, 159. 

Stars, distance of, 150. 

Stars, double, 160. 

Stars, greatest number seen, 59. 

Stars, least number seen, 59. 

Stars, magnitudes, 151. 

Stars mentioned in Bible, 159. 

Stars, names of, 151. 

Stars, number of, 150. 

Stars, variable, 160. 

Summer, length of, 48. 

Sun, angular diameter of, 44. 

Sun, apparent motion of, 42. 

Sun, description of, 93. 

Sun-dial, 174-176. 

Sun, diameter in miles, 95. 

Sun, heat of, no. 

Sun, if inhabited, 99. 

Sun, midnight, 54. 

Sun's distance, how found, 94. 

Sun's hour angle, 171. 

Sun's influence, no. 

Sun's parallax, how calculated, 

95- 
Sun's photosphere, 101. 
Sun's rising point, 101. 



Surface of moon, 88. 
Syzygies, 68. 

Telescope, 199. 

Telescope, first used, 134. 

Terminology, 18. 

Tides, 90. 

Time, measurement of, 168. 

Time, natural standard of, 168. 

Time of sunrise, 175. 

Time, standard, 183. 

Time, standard of, 24, 168. 

Trade winds, 212. 

Transit instrument, 199. 

Transit of Venus, 94. 

Tropics, 40. 

Twilight, calculation of, 52. 

Ulloa, 37. 

Universal day, 188. 
Universal hour, 187. 
Uranus, description of, 130. 
Uranus, discovery of, 114. 
Ursa, Major, 156. 

Variation of the compass, 214. 
Velocity of earth in its orbit, 

Velocity of earth round its axis, 

63- 

Velocity of light, 134. 

Velocity of light, how discov- 
ered, 135. 

Venus, description of, 122. 

Venus, distance from earth cal- 
culated, 126. 

Venus, transits of, 94, 96. 

Verifying the chronometer, 240. 

Voyage of Columbus, 206. 

Voyages, Arctic, 57. 

Voyages, Chinese, 202. 

Voyages, Phoenicians, 202. 



264 



Index. 



Wagon, 166. 
Wane, 71. 
Wax, 71. 
Week, 177. 
Week, days of, 177. 
Winter, length of, 48. 

Year, 24, 178. 

Year, anomalistic, 179. 



Year, sidereal, 179. 
Year, tropical, 179. 

Zenith, sector, 201. 
Zodiac, 158. 
Zodiac, signs of, 159. 
Zodiacal constellations, 158. 
Zones, 40, 47. 



